Question

How do you solve the following system: #2x-y/2=4, 5x+2y=20 #?

Answer 1

Use linear algebra to solve for x, and then plug the solution back in to solve for y. You will find that `x=36/13` and `y=40/13`.

Explanation:

Let's align the equations, first and foremost:

`2x-y/2=4`
`5x+2y=20`

To eliminate y, we'll multiply the entire top equation by 4, which will make that `-y/2` into `-2y`. We'll then add the two equations together and get a system where it's only x and constants:

`(2x-y/2=4)xx4 rArr 8x-2y=16`

`(8x-2y=16)`
`ul(+(5x+2y=20))`
`13x=36`

`color(red)(x=36/13`

Now, let's plug it back into one of the equations to solve for y:

`5x+2y=20 rArr 5(36/13)+2y=20`

`(5/2)(36/13)+y=10 rArr (5*18)/13+y=10`

`y=10-90/13 rArr y=130/13-90/13=(130-90)/13`

`color(blue)(y=40/13)`