Answer
The solution is $(-1,2)$.
Work Step by Step
The given system of equations is
$-3x-5y=-7$ ...... (1)
$-4x+5y=14$ ...... (2)
Add equation (1) and (2).
$\Rightarrow -3x-5y-4x+5y=-7+14$
Add like terms.
$\Rightarrow -7x=7$
Divide each side by $-7$.
$\Rightarrow \frac{-7x}{-7}=\frac{7}{-7}$
Simplify.
$\Rightarrow x=-1$
Substitute $-1$ for $x$ in equation (2).
$\Rightarrow -4(-1)+5y=14$
Simplify.
$\Rightarrow 4+5y=14$
Subtract $4$ from each side.
$\Rightarrow 4+5y-4=14-4$
Simplify.
$\Rightarrow 5y=10$
Divide each side by $5$.
$\Rightarrow \frac{5y}{5}=\frac{10}{5}$
Simplify.
$\Rightarrow y=2$
Check $(x,y)=(-1,2)$
Equation (1):
$\Rightarrow -3x-5y=-7$
$\Rightarrow -3(-1)-5(2)=-7$
$\Rightarrow 3-10=-7$
$\Rightarrow -7=-7$
True.
Equation (2):
$\Rightarrow -4x+5y=14$
$\Rightarrow -4(-1)+5(2)=14$
$\Rightarrow 4+10=14$
$\Rightarrow 14=14$
True.
Hence, the solution is $(-1,2)$.
