Answer
The solution is $(-2,5)$.
Work Step by Step
The given system of equations is
$x+6y=28$ ...... (1)
$2x-3y=-19$ ...... (2)
Multiply equation (2) by $2$.
$\Rightarrow 2(2x-3y)=2(-19)$
Use distributive property.
$\Rightarrow 4x-6y=-38$ ...... (3)
Add equation (1) and (3).
$\Rightarrow x+6y+4x-6y=28-38$
Add like terms.
$\Rightarrow 5x=-10$
Divide each side by $5$.
$\Rightarrow \frac{5x}{5}=-\frac{10}{5}$
Simplify.
$\Rightarrow x=-2$
Substitute $-2$ for $x$ in equation (1).
$\Rightarrow -2+6y=28$
Add $2$ to each side.
$\Rightarrow -2+6y+2=28+2$
Simplify.
$\Rightarrow 6y=30$
Divide each side by $6$.
$\Rightarrow \frac{6y}{6}=\frac{30}{6}$
Simplify.
$\Rightarrow y=5$
Check $(x,y)=(-2,5)$
Equation (1):
$\Rightarrow x+6y=28$
$\Rightarrow -2+6(5)=28$
$\Rightarrow -2+30=28$
$\Rightarrow 28=28$
True.
Equation (2):
$\Rightarrow 2x-3y=-19$
$\Rightarrow 2(-2)-3(5)=-19$
$\Rightarrow -4-15=-19$
$\Rightarrow -19=-19$
True.
Hence, the solution is $(-2,5)$.
