Question

-2x+2y = -22 7x + 10y = -25

Answer 1

`\begin{gathered} \because-2x+2y=-22(1) \\ \because7x+10y=-25(2) \end{gathered}`

To solve this system of equations we must make the coefficients of y equal in values and different in signs, then multiply equation (1) by -5

`\begin{gathered} -2x(-5)+2y(-5)=-22(-5) \\ 10x-10y=110(3) \end{gathered}`

Add equations (2), (3) to eliminate y

`\begin{gathered} (7x+10x)+(10y-10y)=(-25+110) \\ 17x+0=85 \\ 17x=85 \end{gathered}`

Now divide both sides by 17 to find x

`\begin{gathered} (17x)/(17)=(85)/(17) \\ x=5 \end{gathered}`

Substitute the value of x in equation (1) to find the value of y

`\begin{gathered} -2(5)+2y=-22 \\ -10+2y=-22 \end{gathered}`

Add 10 to both sides

`\begin{gathered} -10+10+2y=-22+10 \\ 0+2y=-12 \\ 2y=-12 \end{gathered}`

Divide both sides by 2 to find the value of y

`\begin{gathered} (2y)/(2)=(-12)/(2) \\ y=-6 \end{gathered}`

The solution of the system of equation is (5, -6)