StudySmarter - The all-in-one study app.

4.8 • +11k Ratings

More than 3 Million Downloads

Free

Suggested languages for you:

Americas

Europe

Solving Linear Equations

- Calculus
- Absolute Maxima and Minima
- Absolute and Conditional Convergence
- Accumulation Function
- Accumulation Problems
- Algebraic Functions
- Alternating Series
- Antiderivatives
- Application of Derivatives
- Approximating Areas
- Arc Length of a Curve
- Area Between Two Curves
- Arithmetic Series
- Average Value of a Function
- Calculus of Parametric Curves
- Candidate Test
- Combining Differentiation Rules
- Combining Functions
- Continuity
- Continuity Over an Interval
- Convergence Tests
- Cost and Revenue
- Density and Center of Mass
- Derivative Functions
- Derivative of Exponential Function
- Derivative of Inverse Function
- Derivative of Logarithmic Functions
- Derivative of Trigonometric Functions
- Derivatives
- Derivatives and Continuity
- Derivatives and the Shape of a Graph
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Polar Functions
- Derivatives of Sec, Csc and Cot
- Derivatives of Sin, Cos and Tan
- Determining Volumes by Slicing
- Direction Fields
- Disk Method
- Divergence Test
- Eliminating the Parameter
- Euler's Method
- Evaluating a Definite Integral
- Evaluation Theorem
- Exponential Functions
- Finding Limits
- Finding Limits of Specific Functions
- First Derivative Test
- Function Transformations
- General Solution of Differential Equation
- Geometric Series
- Growth Rate of Functions
- Higher-Order Derivatives
- Hydrostatic Pressure
- Hyperbolic Functions
- Implicit Differentiation Tangent Line
- Implicit Relations
- Improper Integrals
- Indefinite Integral
- Indeterminate Forms
- Initial Value Problem Differential Equations
- Integral Test
- Integrals of Exponential Functions
- Integrals of Motion
- Integrating Even and Odd Functions
- Integration Formula
- Integration Tables
- Integration Using Long Division
- Integration of Logarithmic Functions
- Integration using Inverse Trigonometric Functions
- Intermediate Value Theorem
- Inverse Trigonometric Functions
- Jump Discontinuity
- Lagrange Error Bound
- Limit Laws
- Limit of Vector Valued Function
- Limit of a Sequence
- Limits
- Limits at Infinity
- Limits at Infinity and Asymptotes
- Limits of a Function
- Linear Approximations and Differentials
- Linear Differential Equation
- Linear Functions
- Logarithmic Differentiation
- Logarithmic Functions
- Logistic Differential Equation
- Maclaurin Series
- Manipulating Functions
- Maxima and Minima
- Maxima and Minima Problems
- Mean Value Theorem for Integrals
- Models for Population Growth
- Motion Along a Line
- Motion in Space
- Natural Logarithmic Function
- Net Change Theorem
- Newton's Method
- Nonhomogeneous Differential Equation
- One-Sided Limits
- Optimization Problems
- P Series
- Particle Model Motion
- Particular Solutions to Differential Equations
- Polar Coordinates
- Polar Coordinates Functions
- Polar Curves
- Population Change
- Power Series
- Radius of Convergence
- Ratio Test
- Removable Discontinuity
- Riemann Sum
- Rolle's Theorem
- Root Test
- Second Derivative Test
- Separable Equations
- Separation of Variables
- Simpson's Rule
- Solid of Revolution
- Solutions to Differential Equations
- Surface Area of Revolution
- Symmetry of Functions
- Tangent Lines
- Taylor Polynomials
- Taylor Series
- Techniques of Integration
- The Fundamental Theorem of Calculus
- The Mean Value Theorem
- The Power Rule
- The Squeeze Theorem
- The Trapezoidal Rule
- Theorems of Continuity
- Trigonometric Substitution
- Vector Valued Function
- Vectors in Calculus
- Vectors in Space
- Washer Method
- Decision Maths
- Geometry
- 2 Dimensional Figures
- 3 Dimensional Vectors
- 3-Dimensional Figures
- Altitude
- Angles in Circles
- Arc Measures
- Area and Volume
- Area of Circles
- Area of Circular Sector
- Area of Parallelograms
- Area of Plane Figures
- Area of Rectangles
- Area of Regular Polygons
- Area of Rhombus
- Area of Trapezoid
- Area of a Kite
- Composition
- Congruence Transformations
- Congruent Triangles
- Convexity in Polygons
- Coordinate Systems
- Dilations
- Distance and Midpoints
- Equation of Circles
- Equilateral Triangles
- Figures
- Fundamentals of Geometry
- Geometric Inequalities
- Geometric Mean
- Geometric Probability
- Glide Reflections
- HL ASA and AAS
- Identity Map
- Inscribed Angles
- Isometry
- Isosceles Triangles
- Law of Cosines
- Law of Sines
- Linear Measure and Precision
- Median
- Parallel Lines Theorem
- Parallelograms
- Perpendicular Bisector
- Plane Geometry
- Polygons
- Projections
- Properties of Chords
- Proportionality Theorems
- Pythagoras Theorem
- Rectangle
- Reflection in Geometry
- Regular Polygon
- Rhombuses
- Right Triangles
- Rotations
- SSS and SAS
- Segment Length
- Similarity
- Similarity Transformations
- Special quadrilaterals
- Squares
- Surface Area of Cone
- Surface Area of Cylinder
- Surface Area of Prism
- Surface Area of Sphere
- Surface Area of a Solid
- Surface of Pyramids
- Symmetry
- Translations
- Trapezoids
- Triangle Inequalities
- Triangles
- Using Similar Polygons
- Vector Addition
- Vector Product
- Volume of Cone
- Volume of Cylinder
- Volume of Pyramid
- Volume of Solid
- Volume of Sphere
- Volume of prisms
- Mechanics Maths
- Acceleration and Time
- Acceleration and Velocity
- Angular Speed
- Assumptions
- Calculus Kinematics
- Coefficient of Friction
- Connected Particles
- Conservation of Mechanical Energy
- Constant Acceleration
- Constant Acceleration Equations
- Converting Units
- Elastic Strings and Springs
- Force as a Vector
- Kinematics
- Newton's First Law
- Newton's Law of Gravitation
- Newton's Second Law
- Newton's Third Law
- Power
- Projectiles
- Pulleys
- Resolving Forces
- Statics and Dynamics
- Tension in Strings
- Variable Acceleration
- Work Done by a Constant Force
- Probability and Statistics
- Bar Graphs
- Basic Probability
- Charts and Diagrams
- Conditional Probabilities
- Continuous and Discrete Data
- Frequency, Frequency Tables and Levels of Measurement
- Independent Events Probability
- Line Graphs
- Mean Median and Mode
- Mutually Exclusive Probabilities
- Probability Rules
- Probability of Combined Events
- Quartiles and Interquartile Range
- Systematic Listing
- Pure Maths
- ASA Theorem
- Absolute Value Equations and Inequalities
- Addition and Subtraction of Rational Expressions
- Addition, Subtraction, Multiplication and Division
- Algebra
- Algebraic Fractions
- Algebraic Notation
- Algebraic Representation
- Analyzing Graphs of Polynomials
- Angle Measure
- Angles
- Angles in Polygons
- Approximation and Estimation
- Area and Circumference of a Circle
- Area and Perimeter of Quadrilaterals
- Area of Triangles
- Argand Diagram
- Arithmetic Sequences
- Average Rate of Change
- Bijective Functions
- Binomial Expansion
- Binomial Theorem
- Chain Rule
- Circle Theorems
- Circles
- Circles Maths
- Combination of Functions
- Combinatorics
- Common Factors
- Common Multiples
- Completing the Square
- Completing the Squares
- Complex Numbers
- Composite Functions
- Composition of Functions
- Compound Interest
- Compound Units
- Conic Sections
- Construction and Loci
- Converting Metrics
- Convexity and Concavity
- Coordinate Geometry
- Coordinates in Four Quadrants
- Cubic Function Graph
- Cubic Polynomial Graphs
- Data transformations
- De Moivre's Theorem
- Deductive Reasoning
- Definite Integrals
- Deriving Equations
- Determinant of Inverse Matrix
- Determinants
- Differential Equations
- Differentiation
- Differentiation Rules
- Differentiation from First Principles
- Differentiation of Hyperbolic Functions
- Direct and Inverse proportions
- Disjoint and Overlapping Events
- Disproof by Counterexample
- Distance from a Point to a Line
- Divisibility Tests
- Double Angle and Half Angle Formulas
- Drawing Conclusions from Examples
- Ellipse
- Equation of Line in 3D
- Equation of a Perpendicular Bisector
- Equation of a circle
- Equations
- Equations and Identities
- Equations and Inequalities
- Estimation in Real Life
- Euclidean Algorithm
- Evaluating and Graphing Polynomials
- Even Functions
- Exponential Form of Complex Numbers
- Exponential Rules
- Exponentials and Logarithms
- Expression Math
- Expressions and Formulas
- Faces Edges and Vertices
- Factorials
- Factoring Polynomials
- Factoring Quadratic Equations
- Factorising expressions
- Factors
- Finding Maxima and Minima Using Derivatives
- Finding Rational Zeros
- Finding the Area
- Forms of Quadratic Functions
- Fractional Powers
- Fractional Ratio
- Fractions
- Fractions and Decimals
- Fractions and Factors
- Fractions in Expressions and Equations
- Fractions, Decimals and Percentages
- Function Basics
- Functional Analysis
- Functions
- Fundamental Counting Principle
- Fundamental Theorem of Algebra
- Generating Terms of a Sequence
- Geometric Sequence
- Gradient and Intercept
- Graphical Representation
- Graphing Rational Functions
- Graphing Trigonometric Functions
- Graphs
- Graphs and Differentiation
- Graphs of Common Functions
- Graphs of Exponents and Logarithms
- Graphs of Trigonometric Functions
- Greatest Common Divisor
- Growth and Decay
- Growth of Functions
- Highest Common Factor
- Hyperbolas
- Imaginary Unit and Polar Bijection
- Implicit differentiation
- Inductive Reasoning
- Inequalities Maths
- Infinite geometric series
- Injective functions
- Instantaneous Rate of Change
- Integers
- Integrating Polynomials
- Integrating Trig Functions
- Integrating e^x and 1/x
- Integration
- Integration Using Partial Fractions
- Integration by Parts
- Integration by Substitution
- Integration of Hyperbolic Functions
- Interest
- Inverse Hyperbolic Functions
- Inverse Matrices
- Inverse and Joint Variation
- Inverse functions
- Iterative Methods
- Law of Cosines in Algebra
- Law of Sines in Algebra
- Laws of Logs
- Limits of Accuracy
- Linear Expressions
- Linear Systems
- Linear Transformations of Matrices
- Location of Roots
- Logarithm Base
- Logic
- Lower and Upper Bounds
- Lowest Common Denominator
- Lowest Common Multiple
- Math formula
- Matrices
- Matrix Addition and Subtraction
- Matrix Determinant
- Matrix Multiplication
- Metric and Imperial Units
- Misleading Graphs
- Mixed Expressions
- Modulus Functions
- Modulus and Phase
- Multiples of Pi
- Multiplication and Division of Fractions
- Multiplicative Relationship
- Multiplying and Dividing Rational Expressions
- Natural Logarithm
- Natural Numbers
- Notation
- Number
- Number Line
- Number Systems
- Numerical Methods
- Odd functions
- Open Sentences and Identities
- Operation with Complex Numbers
- Operations with Decimals
- Operations with Matrices
- Operations with Polynomials
- Order of Operations
- Parabola
- Parallel Lines
- Parametric Differentiation
- Parametric Equations
- Parametric Integration
- Partial Fractions
- Pascal's Triangle
- Percentage
- Percentage Increase and Decrease
- Percentage as fraction or decimals
- Perimeter of a Triangle
- Permutations and Combinations
- Perpendicular Lines
- Points Lines and Planes
- Polynomial Graphs
- Polynomials
- Powers Roots And Radicals
- Powers and Exponents
- Powers and Roots
- Prime Factorization
- Prime Numbers
- Problem-solving Models and Strategies
- Product Rule
- Proof
- Proof and Mathematical Induction
- Proof by Contradiction
- Proof by Deduction
- Proof by Exhaustion
- Proof by Induction
- Properties of Exponents
- Proportion
- Proving an Identity
- Pythagorean Identities
- Quadratic Equations
- Quadratic Function Graphs
- Quadratic Graphs
- Quadratic functions
- Quadrilaterals
- Quotient Rule
- Radians
- Radical Functions
- Rates of Change
- Ratio
- Ratio Fractions
- Rational Exponents
- Rational Expressions
- Rational Functions
- Rational Numbers and Fractions
- Ratios as Fractions
- Real Numbers
- Reciprocal Graphs
- Recurrence Relation
- Recursion and Special Sequences
- Remainder and Factor Theorems
- Representation of Complex Numbers
- Rewriting Formulas and Equations
- Roots of Complex Numbers
- Roots of Polynomials
- Roots of Unity
- Rounding
- SAS Theorem
- SSS Theorem
- Scalar Triple Product
- Scale Drawings and Maps
- Scale Factors
- Scientific Notation
- Second Order Recurrence Relation
- Sector of a Circle
- Segment of a Circle
- Sequences
- Sequences and Series
- Series Maths
- Sets Math
- Similar Triangles
- Similar and Congruent Shapes
- Simple Interest
- Simplifying Fractions
- Simplifying Radicals
- Simultaneous Equations
- Sine and Cosine Rules
- Small Angle Approximation
- Solving Linear Equations
- Solving Linear Systems
- Solving Quadratic Equations
- Solving Radical Inequalities
- Solving Rational Equations
- Solving Simultaneous Equations Using Matrices
- Solving Systems of Inequalities
- Solving Trigonometric Equations
- Solving and Graphing Quadratic Equations
- Solving and Graphing Quadratic Inequalities
- Special Products
- Standard Form
- Standard Integrals
- Standard Unit
- Straight Line Graphs
- Substraction and addition of fractions
- Sum and Difference of Angles Formulas
- Sum of Natural Numbers
- Surds
- Surjective functions
- Tables and Graphs
- Tangent of a Circle
- The Quadratic Formula and the Discriminant
- Transformations
- Transformations of Graphs
- Translations of Trigonometric Functions
- Triangle Rules
- Triangle trigonometry
- Trigonometric Functions
- Trigonometric Functions of General Angles
- Trigonometric Identities
- Trigonometric Ratios
- Trigonometry
- Turning Points
- Types of Functions
- Types of Numbers
- Types of Triangles
- Unit Circle
- Units
- Variables in Algebra
- Vectors
- Verifying Trigonometric Identities
- Writing Equations
- Writing Linear Equations
- Statistics
- Bias in Experiments
- Binomial Distribution
- Binomial Hypothesis Test
- Bivariate Data
- Box Plots
- Categorical Data
- Categorical Variables
- Central Limit Theorem
- Chi Square Test for Goodness of Fit
- Chi Square Test for Homogeneity
- Chi Square Test for Independence
- Chi-Square Distribution
- Combining Random Variables
- Comparing Data
- Comparing Two Means Hypothesis Testing
- Conditional Probability
- Conducting a Study
- Conducting a Survey
- Conducting an Experiment
- Confidence Interval for Population Mean
- Confidence Interval for Population Proportion
- Confidence Interval for Slope of Regression Line
- Confidence Interval for the Difference of Two Means
- Confidence Intervals
- Correlation Math
- Cumulative Distribution Function
- Cumulative Frequency
- Data Analysis
- Data Interpretation
- Degrees of Freedom
- Discrete Random Variable
- Distributions
- Dot Plot
- Empirical Rule
- Errors in Hypothesis Testing
- Estimator Bias
- Events (Probability)
- Frequency Polygons
- Generalization and Conclusions
- Geometric Distribution
- Histograms
- Hypothesis Test for Correlation
- Hypothesis Test for Regression Slope
- Hypothesis Test of Two Population Proportions
- Hypothesis Testing
- Inference for Distributions of Categorical Data
- Inferences in Statistics
- Large Data Set
- Least Squares Linear Regression
- Linear Interpolation
- Linear Regression
- Measures of Central Tendency
- Methods of Data Collection
- Normal Distribution
- Normal Distribution Hypothesis Test
- Normal Distribution Percentile
- Paired T-Test
- Point Estimation
- Probability
- Probability Calculations
- Probability Density Function
- Probability Distribution
- Probability Generating Function
- Quantitative Variables
- Quartiles
- Random Variables
- Randomized Block Design
- Residual Sum of Squares
- Residuals
- Sample Mean
- Sample Proportion
- Sampling
- Sampling Distribution
- Scatter Graphs
- Single Variable Data
- Skewness
- Spearman's Rank Correlation Coefficient
- Standard Deviation
- Standard Error
- Standard Normal Distribution
- Statistical Graphs
- Statistical Measures
- Stem and Leaf Graph
- Sum of Independent Random Variables
- Survey Bias
- T-distribution
- Transforming Random Variables
- Tree Diagram
- Two Categorical Variables
- Two Quantitative Variables
- Type I Error
- Type II Error
- Types of Data in Statistics
- Variance for Binomial Distribution
- Venn Diagrams

Assuming we were to order a slice of pizza that cost £25, and donuts that also costs £20 for one. If all the money we budgeted was £1000, how much of each can we order?

This system can be modelled mathematically into a linear equation as

$25x+20y=1000$,

where x and y could be found, considering$x=numberofpizzaslices$ and $y=numberofdonuts$.

In this article, we will learn about solving linear equations, using different methods to solve them, and how to verify their solutions.

A **linear equation**, also known as a one-degree equation, is an equation in which the highest power of the variable is always 1.

Linear equations in **one variable** are in **standard form** as

$ax+b=0$,

where **x** is a variable, **a** is a coefficient and **b** is a constant.

They are in **two variable** **standard form** as

$ax+by=c$,

where **x** and **y** are variables, **c** is a constant, and **a** and **b** are coefficients.

They are linear because both their variables have power 1, and graphing these equations is always in a straight line.

Solving linear equations involves finding the values of the variables such that the equation is satisfied when they are substituted back into them. The fundamental rule that is required to solve them is "the golden rule". This states that you do unto one side of the equation what you do unto the other side of the equation.

Linear equations in one variable as discussed earlier in this article are in the form

$ax+b=0$,

where **x** is a variable, **a** is a coefficient and **b** is a constant.

These equations are solved easily by grouping like terms first. This means the terms with the variable will be sent to one side of the equation, whilst the constants go to the other side. Then, they can now be operated to find the value of the variable.

The steps that are associated with solving linear equations in one variable are:

Simplify each side of the equation if need be;

Isolate the variable;

Algebraically find the value of the variable;

Verify your solution by substituting the value back into the equation.

Let us take an example below.

Solve the equation$3x+2=0$.

**Solution**

$3x+2=0$

Each side of the equation is simplified, **step 1** is achieved.

**Step 2**: Group like terms by subtracting 2 from each side of the equation

$3x+2-2=0-2$

$3x=-2$

**Step 3**: Divide each side by 3

$\frac{3x}{3}=\frac{-2}{3}$

$x=\frac{-2}{3}$

**Step 4**: Now we can evaluate this to see if this is true. The equation means that everything on the left side should be equal to what is on the right. Hence, everything on the left side of the equation should be equal to 0. We will substitute the solution into the equation now.

$3x+2=0\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}3\left(\frac{-2}{3}\right)+2=0$

We will now divide 3 outside the bracket by the 3 as the denominator, and we will have 1 each.

$-2+2=0$

$0=0$

We see here that the solution we have is true.

Solve the equation $x+7=18$.

**Solution**

Each side of the equation is simplified, **step 1** is achieved.

**Step 2 and 3**: Group like terms by subtracting 7 from each side of the equation

$x+7-7=18-7$

$x=11$

**Step 4**: Now we can evaluate this to see if this is true. The equation means that everything on the left side should be equal to what is on the right. Hence if we add x to 7, we should have 18

$x+7=18$

$x=11$

$11+7=18$

This means our equation is true.

Solving linear equations in two variables can no longer give you absolute values unless another equation is provided that possesses the same variables as the first equation. For instance, if we were given an equation as

$x+y=5$,

then, if x = 3, y = 2, if x = 4, y = 1, and so on.

The only way we can have absolute values is to have another equation with the same variables.

One way to solve this type of equation is by substitution method. You make one variable the subject of one of the equations and substitute that value into the other equation to have only one variable to find. We can take the example below.

Solve for x and y given the equations $2x+5y=20$ and $3x+5y=12$.

**Solution**

$\left\{\begin{array}{l}2x+5y=20\\ 3x+5y=12\end{array}\right.$

Let us make y the subject of the first equation by subtracting 2x from each side of the equation.

$2x-2x+5y=20-2x$

$5y=20-2x$$\frac{5y}{5}=\frac{20}{5}-\frac{2x}{5}$$y=4-\frac{2x}{5}$Now we will substitute this value of y into the second equation

$3x+5y=12$

$3x+5(4-\frac{2x}{5})=12$$3x+20-2x=12$$x=12-20$$x=-8$We will now substitute this value for x into any of the equations to find y. We will use the first.

$2x+5y=20$

$2(-8)+5y=20$$-16+5y=20$Add 16 to each side of the equation to make 5y stand alone on that side of the equation

$16-16+5y=20+16$

$5y=36$Divide through by 5 to find y

$\frac{5y}{5}=\frac{36}{5}\phantom{\rule{0ex}{0ex}}$

$y=\frac{36}{5}$

Linear equations in two variables are such that both equations would remain true when we find a solution for each variable. When we want to solve systems of linear equations by graphing, we plot both equations on the same coordinate plane. Now the point where both lines intersect is the solution for the system. Let us look at the example below.

Solve the equation

$\left\{\begin{array}{l}y-2x=2\\ -x=-y-1\end{array}\right.$

**Solution**

As mentioned earlier, we will want to plot both equations on the coordinate plane. We will start by finding the y-intercept and slope for each line. This means for each equation, we will rewrite it in the slope-intercept form. Slope intercept form is given by;

$y=mx+b$

where m is the slope

b is the y-intercept

x is the x-value on the coordinate plane

y is the y-value on the coordinate plane

$y-2x=2$ [Equation 1]

$y=2x+2$

This means that;

$m=2$

$y-intercept=2$

$-x=-y-1$ [Equation 2]

$y=x-1$

This means that;

$m=1$

$y-intercept=-1$

Both equations in the slope-intercept form are given by;

$\left\{\begin{array}{l}y=2x+2\\ y=x-1\end{array}\right.$

Let us find the *y-*value by assuming two values on the x-axis. Recall that two points are enough to give us a line. Given two values on the x-axis, we will use 1 and 2, what is y when x = 1? And what is y when x = 2?

The solution to these two questions should give us the lines of both equations.

Let us start with Equation 1,

$y=2x+2$.

Substitute 1 into the equation assuming x = 1,

$y=2\left(1\right)+2$

$y=4$

When $x=1$, $y=4$.

Substitute 2 into the equation assuming x = 2,

$y=2\left(2\right)+2$

$y=6$

When $x=2$, $y=6$.

We now have two points for Equation 1 to be plotted.

The same will be done for the Equation 2,

$y=x-1$.

Substitute 1 into the equation assuming x = 1,

$y=1-1$

$y=0$

When $x=1$, $y=0$.

Substitute 2 into the equation assuming x = 2,

$y=2-1$

$y=1$

When $x=2$, $y=1$.

Let us plot these points and draw the line on the same coordinate plane.

The point they both intercept is the solution for the problem, (–3, –4).

This means

$x=-3$

$y=-4$

Now we can evaluate this to see if this is true. Working with equations means that everything on the left side should be equal to what is on the right. Since we have two equations here, we will verify both. Let us start with the first one.

$y-2x=2$

We will substitute the values we just found into the equation

$-4-2(-3)=2$

Since both negative values are multiplying each other, the result becomes positive.

$-4+6=2$

$2=2$.

We do see here that the first equation is satisfied. We can go ahead to do the same with the second equation.

$-x=-y-1$

Substitute the values we just found into the equation

$-(-3)=-(-4)-1$

Negative values multiplying each other will result in positive.

$3=4-1$

$3=3$

We do realize here that the solution satisfies both equations, therefore, the solution is correct.

- Linear equations are equations that have the highest power of the variable is always 1.
- Linear equations in one variable are in standard form as ax + b = 0, where x is a variable, a is a coefficient and b is a constant.
- They are in two variable standard form as ax + by = c, where x and y are variables, c is a constant, and a and b are coefficients.
- Solving for linear equations in one variable means finding for that variable by making it the subject and performing the necessary arithmetics.
- Solving for linear equations in two variables requires another equation to have an absolute solution for variables.

A linear equation is one in which the highest power of the variable is always 1.

Here are two examples:

2x – 4 = 7

5 – 4y – 3 = 12

Graphing, substitution, and elimination.

The following steps provide a good method to use when solving linear equations.

(1) Simplify each side of the equation by removing parentheses and combining like terms.

(2) Use addition or subtraction to isolate the variable term on one side of the equation.

(3) Use multiplication or division to solve for the variable.

More about Solving Linear Equations

Be perfectly prepared on time with an individual plan.

Test your knowledge with gamified quizzes.

Create and find flashcards in record time.

Create beautiful notes faster than ever before.

Have all your study materials in one place.

Upload unlimited documents and save them online.

Identify your study strength and weaknesses.

Set individual study goals and earn points reaching them.

Stop procrastinating with our study reminders.

Earn points, unlock badges and level up while studying.

Create flashcards in notes completely automatically.

Create the most beautiful study materials using our templates.

Sign up to highlight and take notes. It’s 100% free.

Over 10 million students from across the world are already learning smarter.

Get Started for Free