Answer
The solution is $(3,22)$.
Work Step by Step
The given system of equations is
$\Rightarrow -5x+3y=51$ ...... (1)
$\Rightarrow y=10x-8$ ...... (2)
Substitute $10x-8$ for $y$ in equation (1).
$\Rightarrow -5x+3(10x-8)=51$
Use distributive property.
$\Rightarrow -5x+30x-24=51$
Add like terms.
$\Rightarrow 25x-24=51$
Add $24$ to each side.
$\Rightarrow 25x-24+24=51+24$
Simplify.
$\Rightarrow 25x=75$
Divide each side by $25$.
$\Rightarrow \frac{25x}{25}=\frac{75}{25}$
Simplify.
$\Rightarrow x=3$
Substitute $3$ for $x$ in equation (2).
$\Rightarrow y=10(3)-8$
Simplify.
$\Rightarrow y=30-8$
$\Rightarrow y=22$
Check
Equation (1)
$\Rightarrow -5x+3y=51$
$\Rightarrow -5(3)+3(22)=51$
$\Rightarrow -15+66=51$
$\Rightarrow 51=51$
True.
Check
Equation (2)
$\Rightarrow y=10x-8$
$\Rightarrow 22=10(3)-8$
$\Rightarrow 22=30-8$
$\Rightarrow 22=22$
True.
Hence, the solution is $(3,22)$.
