Question

Solve the following system using elimination 2x+4y=8 6x+10y=30

Answer 1

So to use the elimination method, we need to put these equations on top of each other so that we can eliminate a variable:

`2x+4y=8`

`6x+10y=30`

If we multiply the top equation by -3, we can eliminate the x variable:

`-3(2x+4y=8)`

`6x+10y=30`

And we simplify. Then we add the two equations together:

`-6x-12y=-24`

+
`6x+10y=30`

---------------------------------

`-2y=6`

Then we solve for y:

`y=-3`

Then we need to return to one of the original equations (either will work) and plug y in. Then we will solve for x. Let's choose the first equation:

`2x+4y=8`

`2x+4(-3)=8`

`2x-12=8`

`2x=20`

`x=10`

So now we know that our solution is: (10, -3).