Answer
The solution is $(-3,29)$.
Work Step by Step
The given system of equations is
$9x+y=2$ ...... (1)
$-4x-y=-17$ ...... (2)
Add equation (1) and (2).
$\Rightarrow 9x+y-4x-y=2-17$
Add like terms.
$\Rightarrow 5x=-15$
Divide each side by $5$.
$\Rightarrow \frac{5x}{5}=\frac{-15}{5}$
Simplify.
$\Rightarrow x=-3$
Substitute $-3$ for $x$ equation (1).
$\Rightarrow 9(-3)+y=2$
Simplify.
$\Rightarrow -27+y=2$
Add $27$ to each side.
$\Rightarrow -27+y+27=2+27$
Simplify.
$\Rightarrow y=29$
Check $(x,y)=(-3,29)$
Equation (1):
$\Rightarrow 9x+y=2$
$\Rightarrow 9(-3)+29=2$
$\Rightarrow -27+29=2$
$\Rightarrow 2=2$
True.
Equation (2):
$\Rightarrow -4x-y=-17$
$\Rightarrow -4(-3)-29=-17$
$\Rightarrow 12-29=-17$
$\Rightarrow -17=-17$
True.
Hence, the solution is $(-3,29)$.
