Question

How do you solve the system of equations `4x + 10y = 4` and `8x + 20y = 8`?

Answer 1

`x=1, y=0`

Explanation:

`color(white)(-)4x+10y=4`
`color(white)(-)`
`color(white)(-)8x+10y=8`

Let's use elimination to solve this!

I'm going to multiply the top equation by `1/2` to change all the `y`s to `10y`:

`1/2 xxcolor(white)()(4x+10y=4)`
`color(black)(-)`
`color(white)(1/2 xx)8x+10y=8`
....................................

becomes

`color(white)(-)2x+10y=2`
`color(black)(-)`
`color(white)(-)8x+10y=8`
........................................
`-6x=-6`

divide by `-6` on both sides

`x=1`

Now let's solve for `y`:

`4x+10y=4`

`4(1)+10y=4`

`4+10y=4`

subtract `4` on both sides

`10y=0`

divide by `10` on both sides

`y=0`

Just to check our work, let's solve for the other equation, replacing `x` and `y` with `1` and `0`:

`8x+10y=8`

`8(1)+10(0)` should equal `8`

`8+0` does equal `8`! We were right!