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Found in: Page 795

### Precalculus Enhanced with Graphing Utilities

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

# In Problems 1–4, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.$\left\{\begin{array}{l}-2x+y=-7\\ 4x+3y=9\end{array}\right\$

The solution of the system of equations $\left\{\begin{array}{l}-2x+y=-7\\ 4x+3y=9\end{array}\right\$ is $\left(3,-1\right)$

See the step by step solution

## Step 1. Given

The system of equations:

$\left\{\begin{array}{l}-2x+y=-7\\ 4x+3y=9\end{array}\right\$

## Step 2. Solve the equation

Multiply the first equation by $2$,

$-4x+2y=-14$

Add the above equation with second equation, we get,

$5y=-5\phantom{\rule{0ex}{0ex}}y=-1$

## Step 3. Find x

Substitute $y=-1$ in the second equation,

$4x+3y=9\phantom{\rule{0ex}{0ex}}4x+3\left(-1\right)=9\phantom{\rule{0ex}{0ex}}4x=12\phantom{\rule{0ex}{0ex}}x=3$

## Step 4. Check the solution

Substitute $x=3;y=-1$ in the first equation,

$-2x+y=-7\phantom{\rule{0ex}{0ex}}-2\left(3\right)+\left(-1\right)=-7\phantom{\rule{0ex}{0ex}}-7=-7$

Hence the solution is checked.