Answer
The solution is $(2,3)$.
Work Step by Step
The given system of equations is
$2x-3y=-5$ ...... (1)
$5x+2y=16$ ...... (2)
Multiply equation (1) by $2$.
$2(2x-3y)=2(-5)$
Use distributive property.
$4x-6y=-10$ ...... (3)
Multiply equation (2) by $3$.
$3(5x+2y)=3(16)$
Use distributive property.
$15x+6y=48$ ...... (4)
Add equation (3) and (4).
$\Rightarrow 4x-6y+15x+6y=-10+48$
Add like terms.
$\Rightarrow 19x=38$
Divide each side by $19$.
$\Rightarrow \frac{19x}{19}=\frac{38}{19}$
Simplify.
$\Rightarrow x=2$
Substitute $2$ for $x$ in equation (2).
$\Rightarrow 5(2)+2y=16$
Simplify.
$\Rightarrow 10+2y=16$
Subtract $10$ from each side.
$\Rightarrow 10+2y-10=16-10$
Simplify.
$\Rightarrow 2y=6$
Divide each side by $2$.
$\Rightarrow \frac{2y}{2}=\frac{6}{2}$
Simplify.
$\Rightarrow y=3$
Check $(x,y)=(2,3)$
Equation (1):
$\Rightarrow 2x-3y=-5$
$\Rightarrow 2(2)-3(3)=-5$
$\Rightarrow 4-9=-5$
$\Rightarrow -5=-5$
True.
Equation (2):
$\Rightarrow 5x+2y=16$
$\Rightarrow 5(2)+2(3)=16$
$\Rightarrow 10+6=16$
$\Rightarrow 16=16$
True.
Hence, the solution is $(2,3)$.
