Chapter 12.8, Problem 6MRE

To determine

To calculate: The solution set for the system of equations with the help either substitution or elimination.

  $\begin{array}{l}x+y=3\\ 2x+3y=-2\end{array}$

Answer to Problem 6MRE

The solution set for the system of equations is $\left(11,-8\right)$ .

Explanation of Solution

Given information:

The system of equations

  $\begin{array}{l}x+y=3\\ 2x+3y=-2\end{array}$

Calculation:

Consider the system of equations

  $\begin{array}{l}x+y=3\\ 2x+3y=-2\end{array}$

Use the method of substitution to solve the system above.

From the equation $x+y=3$ isolate the value of y ,

  $\begin{array}{c}x+y=3\\ y=3-x\end{array}$

Now substitute $y=3-x$ in the equation $2x+3y=-2$ ,

  $\begin{array}{c}2x+3y=-2\\ 2x+3\left(3-x\right)=-2\\ 2x+9-3x=-2\\ -x+9=-2\end{array}$

Simplified further:

  $\begin{array}{c}-x+9=-2\\ -x=-2-9\\ -x=-11\\ x=11\end{array}$

Now, substitute $x=11$ in the equation $y=3-x$ ,

  $\begin{array}{c}y=3-x\\ y=3-11\\ y=-8\end{array}$

Therefore, solution is the coordinate pair, $\left(11,-8\right)$ .

Thus, the solution set for the system of equations is $\left(11,-8\right)$ .