Question

x - 2y = -7\
x + 2y = 5

Explanation:

Step1: Add the two equations

We have the system of equations:

$$\begin{cases} x - 2y = -7 \\ x + 2y = 5 \end{cases}$$

Adding the two equations together: $(x - 2y)+(x + 2y)=-7 + 5$.
Simplifying the left - hand side: $x - 2y+x + 2y = 2x$, and the right - hand side: $-7 + 5=-2$. So we get $2x=-2$.

Step2: Solve for x

Divide both sides of the equation $2x=-2$ by 2: $x=\frac{-2}{2}=-1$.

Step3: Substitute x into one of the original equations to solve for y

Substitute $x = - 1$ into the equation $x + 2y = 5$. We have $-1+2y = 5$.
Add 1 to both sides of the equation: $2y=5 + 1=6$.
Divide both sides by 2: $y=\frac{6}{2}=3$.

Answer:

The solution to the system of equations is $x=-1,y = 3$.