Answered

how would i solve


4x-3y=8

5x-2y=-11


using the elimination method?

i'm in algebra 1 and we had a sub the day we were doing this and he was terrible explaining the situations on the worksheet. please explain

Verified Answer :

naǫ

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:
\(x=-7 \\ y=-12\)

Answer:

x=-7 and y=-12

Step-by-step explanation:

Related Questions