To use the elimination method, the coefficient of one variable in one equation must be the opposite number of the coefficient of the same variable in the second equation.
[tex]4x-3y=8 \\
5x-2y=-11[/tex]
Here you can multiply the first equation by 2, and the second equation by -3.
[tex]4x-3y=8 \ \ |\cdot 2 \\
5x-2y=-11 \ \ |\cdot (-3) \\ \\
8x-6y=16 \\
-15x+6y=33[/tex]
Now you just add the equations by sides and solve for one variable.
[tex]8x-6y=16 \\ \underline{-15x+6y=33 } \\
8x-6y-15x+6y=16+33 \\
8x-15x=16+33 \\
-7x=49 \\
x=-7[/tex]
Now you solve for the other variable by substituting -7 for x in one of the equations.
[tex]4x-3y=8 \\
4 \cdot (-7)-3y=8 \\
-28-3y=8 \\
-3y=8+28 \\
-3y=36 \\
y=-12[/tex]
You could choose x at the beginning as well. Then you'd have:
[tex]4x-3y=8 \ \ |\cdot (-5)\\
5x-2y=-11 \ \ |\cdot 4 \\ \\
-20x+15y=-40 \\
\underline{20x-8y=-44 \ \ \ \ \ \ } \\
-20x+15y+20x-8y=-40-44 \\
15y-8y=-40-44 \\
7y=-84 \\
y=-12 \\ \\
4x-3y=8 \\
4x-3 \cdot (-12)=8 \\
4x+36=8 \\
4x=8-36 \\
4x=-28 \\
x=-7[/tex]
So the answer is:
[tex]x=-7 \\ y=-12[/tex]
