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Q. 19

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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}5x-y=21\\ 2x+3y=-12\end{array}\right\$

The solution of the given system of equation is $x=3,y=-6;\left(3,-6\right)$.

See the step by step solution

## Step 1. Given information.

The given equations are:

$\begin{array}{rcl}5x-y& =& 21\\ 2x+3y& =& -12\end{array}$

## Step 2. Determine the value of one variable by substitution.

The first equation can be written as:

$\begin{array}{rcl}-y& =& 21-5x\\ y& =& 5x-21\end{array}$

Substitute this in the second equation.

$\begin{array}{rcl}2x+3\left(5x-21\right)& =& -12\\ 2x+15x-63& =& -12\\ 17x& =& -12+63\\ x& =& \frac{51}{17}\\ x& =& 3\end{array}$

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

Substitute $x=3$ in $y=5x-21$.

$\begin{array}{rcl}y& =& 5\left(3\right)-21\\ & =& 15-21\\ & =& -6\end{array}$

The solution of the given system of equation is role="math" $x=3,y=-6;\left(3,-6\right)$.