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### 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}{r}x+2y=-7\\ x+y=-3\end{array}\right\$

The solution of the given system of equation is $x=1,y=-4;\left(1,-4\right)$.

See the step by step solution

## Step 1. Given information.

The given equations are:

$\begin{array}{rcl}x+2y& =& -7\\ x+y& =& -3\end{array}$

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

The second equation can be written as:

$x=-3-y$

Substitute this in the first equation.

$\begin{array}{rcl}\left(-3-y\right)+2y& =& -7\\ -3+y& =& -7\\ y& =& -7+3\\ y& =& -4\end{array}$

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

Substitute $y=-4$ in $x=-3-y$.

$\begin{array}{rcl}x& =& -3-\left(-4\right)\\ & =& -3+4\\ & =& 1\end{array}$

The solution of the given system of equation is $x=1,y=-4;\left(1,-4\right)$.