Answer
The solution is $(5,3)$.
Work Step by Step
The given system of equations is
$\Rightarrow x=17-4y$ ...... (1)
$\Rightarrow y=x-2$ ...... (2)
Substitute $x-2$ for $y$ in equation (1).
$\Rightarrow x=17-4(x-2)$
Use distributive property.
$\Rightarrow x=17-4x+8$
Add like terms.
$\Rightarrow x=25-4x$
Add $4x$ to each side.
$\Rightarrow x+4x=25-4x+4x$
Simplify.
$\Rightarrow 5x=25$
Divide each side by $5$.
$\Rightarrow \frac{5x}{5}=\frac{25}{5}$
Simplify.
$\Rightarrow x=5$
Substitute $5$ for $x$ in equation (2).
$\Rightarrow y=5-2$
Simplify.
$\Rightarrow y=3$
Check
Equation (1)
$\Rightarrow x=17-4y$
$\Rightarrow 5=17-4(3)$
$\Rightarrow 5=17-12$
$\Rightarrow 5=5$
True.
Check
Equation (2)
$\Rightarrow y=x-2$
$\Rightarrow 3=5-2$
$\Rightarrow 3=3$
True.
Hence, the solution is $(5,3)$.
