Answer
The solution is $(2,-8)$.
Work Step by Step
The given system of equations is
$9x-2y=34$ ...... (1)
$5x+2y=-6$ ...... (2)
Add equation (1) and (2).
$\Rightarrow 9x-2y+5x+2y=34-6$
Add like terms.
$\Rightarrow 14x=28$
Divide each side by $14$.
$\Rightarrow \frac{14x}{14}=\frac{28}{14}$
Simplify.
$\Rightarrow x=2$
Substitute $2$ for $x$ in equation (2).
$\Rightarrow 5(2)+2y=-6$
Simplify.
$\Rightarrow 10+2y=-6$
Subtract $10$ from each side.
$\Rightarrow 10+2y-10=-6-10$
Simplify.
$\Rightarrow 2y=-16$
Divide each side by $2$.
$\Rightarrow \frac{2y}{2}=-\frac{16}{2}$
Simplify.
$\Rightarrow y=-8$
Check $(x,y)=(2,-8)$
Equation (1):
$\Rightarrow 9x-2y=34$
$\Rightarrow 9(2)-2(-8)=34$
$\Rightarrow 18+16=34$
$\Rightarrow 34=34$
True.
Equation (2):
$\Rightarrow 5x+2y=-6$
$\Rightarrow 5(2)+2(-8)=-6$
$\Rightarrow 10-16=-6$
$\Rightarrow -6=-6$
True.
Hence, the solution is $(2,-8)$.
