Answer
$(2,-2)$
Work Step by Step
The given system of equations is
$\Rightarrow -x+y=-4$ ...... (1)
$\Rightarrow 4x-y=10$ ...... (2)
Solve for $y$ in equation (1).
$\Rightarrow y=-4+x$ ...... (3)
Substitute $-4+x$ for $y$ in equation (2).
$\Rightarrow 4x-(-4+x)=10$
Clear the parentheses.
$\Rightarrow 4x+4-x=10$
Add like terms.
$\Rightarrow 3x+4=10$
Subtract $4$ from each side.
$\Rightarrow 3x+4-4=10-4$
Simplify.
$\Rightarrow 3x=6$
Divide each side by $3$.
$\Rightarrow \frac{3x}{3}=\frac{6}{3}$
Simplify.
$\Rightarrow x=2$
Substitute $2$ for $x$ in equation (3).
$\Rightarrow y=-4+2$
Simplify.
$\Rightarrow y=-2$
Check
Equation (1)
$\Rightarrow -x+y=-4$
$\Rightarrow -2-2=-4$
$\Rightarrow -4=-4$
True.
Check
Equation (2)
$\Rightarrow 4(2)-(-2)=10$
$\Rightarrow 8+2=10$
$\Rightarrow 10=10$
True.
Hence, the solution is $(2,-2)$.
