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Q. 27

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Found in: Page 714

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Solve each system of equations. If the system has no solution, say that it is inconsistent.$\left\{\begin{array}{c}2x-y=0\\ 4x+2y=12\end{array}\right\$

The solution of the given system of equation is $x=1.5,y=3,\left(1.5,3\right)$.

See the step by step solution

## Step 1. Given information.

The given equations are:

$\begin{array}{rcl}2x-y& =& 0\\ 4x+2y& =& 12\end{array}$

## Step 2. Determine one variable in terms of another variable.

The first equation can be written as:

$\begin{array}{rcl}2x-y& =& 0\\ -y& =& -2x\\ y& =& 2x\end{array}$

## Step 3. Determine the value of one variable.

Substitute the above value in the second equation.

$\begin{array}{rcl}4x+2\left(2x\right)& =& 12\\ 4x+4x& =& 12\\ 8x& =& 12\\ x& =& \frac{12}{8}\\ x& =& 1.5\end{array}$

## Step 4. Determine the value of another variable.

Substitute $x=1.5$ in $y=2x$.

$y=2\left(1.5\right)\phantom{\rule{0ex}{0ex}}y=3$

The solution of the given system of equation is $x=1.5,y=3,\left(1.5,3\right)$.