Answer
The system of linear equations has no solution.
Work Step by Step
The given system of equations is
$3x-6y=-9$ ...... (1)
$-5x+10y=10$ ...... (2)
Divide equation (1) by $3$.
$\Rightarrow \frac{3x-6y}{3}=\frac{-9}{3}$
Simplify.
$\Rightarrow x-2y=-3$ ...... (3)
Divide equation (2) by $5$.
$\Rightarrow \frac{-5x+10y}{5}=\frac{10}{5}$
Simplify.
$\Rightarrow -x+2y=2$ ...... (4)
Add equation (3) and (4).
$\Rightarrow x-2y-x+2y=-3+2$
Add like terms.
$\Rightarrow 0=-1$
Subtract $3y$ from each side.
$\Rightarrow 3y-3y=3y+12-3y$
Simplify.
$\Rightarrow 0=12$
The equation $0=12$ is never true.
Hence, the system of linear equations has no solution.
