Question

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

$\left\{\begin{array}{l}-7x+6y=-10\\ x-6y=22\end{array}\right.$

Short answer

The solution of the system is$(x,y)=(-2,-4).$

Step-by-step solution

Step 1. Given Information

The given system is$\left\{\begin{array}{l}-7x+6y=-10\\ x-6y=22\end{array}\right.$

Step 2. Solve for x

$\left\{\begin{array}{l}-7x+6y=-10\\ x-6y=22\end{array}\right.\text{Given}$

Add both equations

$$\begin{gathered} \underline{\begin{array}{l}-7x+6y=-10\\ x-6y=22\end{array}} \\ -6x=12 \\ x=-\frac{12}{6} \\ x=-2 \end{gathered}$$

Step 3. Solve for y

$\begin{array}{l}\\ x-6y=22\text{econdequation}\\ -2-6y=22\\ -6y=22+2\\ -6y=24\\ y=-\frac{24}{6}\\ y=-4\end{array}$

Hence,$(x,y)=(-2,-4)$

Step 4. Verify the solution

$\begin{array}{l}-7x+6y=-10\Rightarrow -7(-2)+6(-4)=-10\\ 14-24=-10\\ -10=-10\text{true}\\ x-6y=22\Rightarrow -2-6(-4)=22\\ -2+24=22\\ 22=22\text{true}\end{array}$

Hence, the solution is$(x,y)=(-2,-4).$