Answer
The solution is $(5,-8)$.
Work Step by Step
The given system of equations is
$\Rightarrow 5x+2y=9$ ...... (1)
$\Rightarrow x+y=-3$ ...... (2)
Isolate $x$ in equation (1).
$\Rightarrow x=-3-y$ ...... (3)
Substitute $-3-y$ for $x$ in equation (1).
$\Rightarrow 5(-3-y)+2y=9$
Simplify.
$\Rightarrow -15-5y+2y=9$
Add like terms.
$\Rightarrow -15-3y=9$
Add $3y-9$ to each side.
$\Rightarrow -15-3y+3y-9=9+3y-9$
Simplify.
$\Rightarrow -24=3y$
Divide each side by $3$.
$\Rightarrow \frac{-24}{3}=\frac{3y}{3}$
Simplify.
$\Rightarrow -8=y$
Substitute $-8$ for $y$ in equation (3).
$\Rightarrow x=-3-(-8)$
Simplify.
$\Rightarrow x=-3+8$
$\Rightarrow x=5$
Check
Equation (1)
$\Rightarrow 5x+2y=9$
$\Rightarrow 5(5)+2(-8)=9$
$\Rightarrow 25-16=9$
$\Rightarrow 9=9$
True.
Check
Equation (2)
$\Rightarrow x+y=-3$
$\Rightarrow 5-8=-3$
$\Rightarrow -3=-3$
True.
Hence, the solution is $(5,-8)$.
