\[\begin{aligned}&3x+2y=-12\\&4x+5y=-23\end{aligned}\]
Available Methods
Substitution
Elimination
Matrix
1
Multiply the 1st row by 4.
12x+8y=−484x+5y=−23\begin{aligned}&12x+8y=-48\\&4x+5y=-23\end{aligned}

2
Multiply the 2nd row by 3.
12x+8y=−4812x+15y=−69\begin{aligned}&12x+8y=-48\\&12x+15y=-69\end{aligned}

3
Subtract the 2nd row from the 1st row.
−7y=21-7y=21

4
Solve for yy in the above equation.
y=−3y=-3

5
Substitute y=−3y=-3 into any of the two equations above
Let's pick the first equation 12x+8y=−4812x+8y=-48.
12x+8×−3=−4812x+8\times -3=-48

6
Solve for xx in the above equation.
x=−2x=-2

7
Therefore,
x=−2y=−3\begin{aligned}&x=-2\\&y=-3\end{aligned}
Done
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