Answer
$(3,-2)$.
Work Step by Step
The given equations are
$\Rightarrow 5x+8y=-1$ ...... (1)
$\Rightarrow 3x+y=7$ ...... (2)
Multiply the second equation by $-8$.
$\Rightarrow -8\cdot (3x+y)=-8\cdot (7)$
Use distributive property.
$\Rightarrow -24x-8y=-56$ ......(3)
Add equation (1) and (3).
$5x+8y-24x-8y=-1-56$
Add like terms.
$-19x=-57$
Divide both sides by $-19$.
$\frac{-19x}{-19}=\frac{-57}{-19}$
Simplify.
$x=3$
Substitute the value of $x$ into equation (2).
$\Rightarrow 3(3)+y=7$
Clear the parentheses.
$\Rightarrow 9+y=7$
Subtract $9$ from both sides.
$\Rightarrow 9+y-9=7-9$
Simplify.
$\Rightarrow y=-2$
Plug $(x,y)=(3,-2)$ into equation (2).
$\Rightarrow 3(3)+(-2)=7$
$\Rightarrow 9-2=7$
$\Rightarrow 7=7$ True.
Solution set is $(3,-2)$.
