Answer
The solution is $(0,-10)$.
Work Step by Step
The given system of equations is
$-y-10=6x$ ...... (1)
$5x+y=-10$ ...... (2)
Add equation (1) and (2).
$\Rightarrow -y-10+5x+y=6x-10$
Add like terms.
$\Rightarrow -10+5x=6x-10$
Add $-5x+10$ to each side.
$\Rightarrow -10+5x-5x+10=6x-10-5x+10$
Simplify.
$\Rightarrow 0=x$
Substitute $0$ for $x$ in equation (2).
$\Rightarrow 5(0)+y=-10$
Simplify.
$\Rightarrow 0+y=-10$
$\Rightarrow y=-10$
Check $(x,y)=(0,-10)$
Equation (1):
$\Rightarrow -y-10=6x$
$\Rightarrow -(-10)-10=6(0)$
$\Rightarrow 10-10=0$
$\Rightarrow 0=0$
True.
Equation (2):
$\Rightarrow 5x+y=-10$
$\Rightarrow 5(0)-10=-10$
$\Rightarrow 0-10=-10$
$\Rightarrow -10=-10$
True.
Hence, the solution is $(0,-10)$.
