Answer
The solution is $(-4,5)$.
Work Step by Step
The given system of equations is
$\Rightarrow x=16-4y$ ...... (1)
$\Rightarrow 3x+4y=8$ ...... (2)
Substitute $16-4y$ for $x$ in equation (2).
$\Rightarrow 3(16-4y)+4y=8$
Use distributive property.
$\Rightarrow 48-12y+4y=8$
Add like terms.
$\Rightarrow 48-8y=8$
Add $8y-8$ to each side.
$\Rightarrow 48-8y+8y-8=8+8y-8$
Simplify.
$\Rightarrow 40=8y$
Divide each side by $8$.
$\Rightarrow \frac{40}{8}=\frac{8y}{8}$
Simplify.
$\Rightarrow 5=y$
Substitute $5$ for $y$ in equation (1).
$\Rightarrow x=16-4(5)$
Simplify.
$\Rightarrow x=16-20$
$\Rightarrow x=-4$
Check
Equation (1)
$\Rightarrow x=16-4y$
$\Rightarrow -4=16-4(5)$
$\Rightarrow -4=16-20$
$\Rightarrow -4=-4$
True.
Check
Equation (2)
$\Rightarrow 3x+4y=8$
$\Rightarrow 3(-4)+4(5)=8$
$\Rightarrow -12+20=8$
$\Rightarrow 8=8$
True.
Hence, the solution is $(-4,5)$.
