Question

Solve using elimination3x+4y=22x+2y=4(?) ()

Answer 1

We have to solve this system of equations using elimination.

In this case, we can eliminate the variable y by substracting two times the second equation from the first one.

Eliminating y means that it will have a coefficient equal to 0. Then, we will have an equation just in terms of x, that can be solved for it.

We can do it as:

`\begin{gathered} 3x+4y-2(2x+2y)=2-2(4) \\ 3x+4y-4x-4y=2-8 \\ (3x-4x)+(4y-4y)=-6 \\ -x=-6 \\ x=6 \end{gathered}`

Knowing x, we can solve for y using any of the two equations:

`\begin{gathered} 2x+2y=4 \\ 2(6)+2y=4 \\ 12+2y=4 \\ 2y=4-12 \\ 2y=-8 \\ y=(-8)/(2) \\ y=-4 \end{gathered}`

Answer: x = 6 and y = -4.