Question

In the following exercises, solve the systems of equations by elimination.

Short answer

The solution of the system is$(x,y)=(-7,-1).$

Step-by-step solution

Step 1. Given information 

The given system is$\left\{\begin{array}{l}x+y=-8\\ x-y=-6\end{array}\right.$

Step 2. Solve for x

$\left\{\begin{array}{l}x+y=-8\\ x-y=-6\end{array}\right.\text{Given}$

Add both equations

$$\begin{gathered} \underline{\begin{array}{l}x+y=-8\\ x-y=-6\end{array}} \\ 2x=-14 \\ x=\frac{-14}{2} \\ x=-7 \end{gathered}$$

Step 3. Solve for y

$\begin{array}{l}x+y=-8\text{firstequation}\\ -7+y=-8\text{Use}x=-7\\ y=-8+7\\ y=-1\end{array}$

Hence,$(x,y)=(-7,-1).$

Step 4. Verify the solution

$\begin{array}{l}x+y=-8\Rightarrow -7-1=-8\\ -8=-8\text{true}\\ x-y=-6\Rightarrow -7-(-1)=-6\\ -7+1=-6\\ -6=-6\text{true}\\ \end{array}$

Hence, the solution is$(x,y)=(-7,-1).$