Answer
The solution is $(1,2)$.
Work Step by Step
The given system of equations is
$12x-7y=-2$ ...... (1)
$8x+11y=30$ ...... (2)
Multiply each side of equation (1) by $-2$.
$-2(12x-7y)=-2(-2)$
Simplify.
$-24x+14y=4$ ...... (3)
Multiply each side of equation (2) by $3$.
$3(8x+11y)=3(30)$
Simplify.
$24x+33y=90$ ...... (4)
Add equation (3) and (4).
$\Rightarrow -24x+14y+24x+33y=4+90$
Add like terms.
$\Rightarrow 47y=94$
Divide each side by $47$.
$\Rightarrow \frac{47y}{47}=\frac{94}{47}$
Simplify.
$\Rightarrow y=2$
Substitute $2$ for $y$ in equation (1).
$\Rightarrow 12x-7(2)=-2$
Simplify.
$\Rightarrow 12x-14=-2$
Add $14$ to each side.
$\Rightarrow 12x-14+14=-2+14$
Simplify.
$\Rightarrow 12x=12$
Divide each side by $12$.
$\Rightarrow \frac{12x}{12}=\frac{12}{12}$
Simplify.
$\Rightarrow x=1$
Check $(x,y)=(1,2)$
Equation (1):
$\Rightarrow 12x-7y=-2$
$\Rightarrow 12(1)-7(2)=-2$
$\Rightarrow 12-14=-2$
$\Rightarrow -2=-2$
True.
Equation (2):
$\Rightarrow 8x+11y=30$
$\Rightarrow 8(1)+11(2)=30$
$\Rightarrow 8+22=30$
$\Rightarrow 30=30$
True.
Hence, the solution is $(1,2)$.
