Question

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

$\left\{\begin{array}{l}3x-2y=1\\ -x+2y=9\end{array}\right.$

Short answer

The solution of the system is$(x,y)=(5,7).$

Step-by-step solution

Step 1. Given Information

The given system is$\left\{\begin{array}{l}3x-2y=1\\ -x+2y=9\end{array}\right.$

Step 2. Solve for x

$\left\{\begin{array}{l}3x-2y=1\\ -x+2y=9\end{array}\right.\text{Given}$

Add both equations

$$\begin{gathered} \underline{\begin{array}{l}3x-2y=1\\ -x+2y=9\end{array}} \\ 2x=10 \\ x=\frac{10}{2} \\ x=5 \end{gathered}$$

Step 3. Solve for y

$\begin{array}{l}3x-2y=1\text{Firstequation}\\ 3\left(5\right)-2y=1\text{Use}x=5\\ 15-2y=1\\ 2y=15-1\\ y=\frac{14}{2}\\ y=7\end{array}$

Hence,$(x,y)=(5,7)$

Step 4. Verify solution

$\begin{array}{l}3x-2y=1\Rightarrow 3\left(5\right)-2\left(7\right)=1\\ 15-14=1\\ 1=1\text{true}\\ \\ -x+2y=9\Rightarrow -5+2\left(8\right)=9\\ -5+16=9\\ 9=9\text{true}\end{array}$

Hence, the solution is$(x,y)=(5,7).$