Given the system of equations:
[tex]\begin{gathered} 4x+6y=-8\ldots(1) \\ 2x+y=12\ldots(2) \end{gathered}[/tex]
Multiply equation (2) with 2.
[tex]4x+2y=24\ldots(3)[/tex]
Subtract (3) from (1) and solve for y.
[tex]\begin{gathered} 4y=-32 \\ y=-\frac{32}{4}=-8 \end{gathered}[/tex]
Substitute the obtained value of y into (2) to find x.
[tex]\begin{gathered} 2x-8=12 \\ 2x=20 \\ x=\frac{20}{2}=10 \end{gathered}[/tex]
The solution of the system of equations is
x = 10, y = -8
