Question

How would i solve

Answer 1

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.

$4x-3y=8 \\ 5x-2y=-11$

Here you can multiply the first equation by 2, and the second equation by -3.

$4x-3y=8 \ \ |\cdot 2 \\ 5x-2y=-11 \ \ |\cdot (-3) \\ \\ 8x-6y=16 \\ -15x+6y=33$

Now you just add the equations by sides and solve for one variable.

$8x-6y=16 \\ \underline{-15x+6y=33 } \\ 8x-6y-15x+6y=16+33 \\ 8x-15x=16+33 \\ -7x=49 \\ x=-7$

Now you solve for the other variable by substituting -7 for x in one of the equations.

$4x-3y=8 \\ 4 \cdot (-7)-3y=8 \\ -28-3y=8 \\ -3y=8+28 \\ -3y=36 \\ y=-12$

You could choose x at the beginning as well. Then you'd have:
$4x-3y=8 \ \ |\cdot (-5)\\ 5x-2y=-11 \ \ |\cdot 4 \\ \\ -20x+15y=-40 \\ \underline{20x-8y=-44 \ \ \ \ \ \ } \\ -20x+15y+20x-8y=-40-44 \\ 15y-8y=-40-44 \\ 7y=-84 \\ y=-12 \\ \\ 4x-3y=8 \\ 4x-3 \cdot (-12)=8 \\ 4x+36=8 \\ 4x=8-36 \\ 4x=-28 \\ x=-7$

So the answer is:
$x=-7 \\ y=-12$