Question

How do you solve the system of equations `x+ 3y = 6` and `- 6x + 2y = 28`?

Answer 1

`x=-3.6, y=-2.3`

Explanation:

Your question: Solve `x+3y=6` and `-6x+2y=28`

Let's solve by eliminating `x`. To do that, we need one `x` value to be negative, and the other positive. Since we already have a negative `x`, let's multiply the `x` on the first equation by 6.

`6x+18y=36`
Then, add the two equations.
`+6x+18y=36`
`-6x+2y=28`

`" "20y=64`

Divide both sides by `20.`

`y=3.2`

Substitute `y=3.2` into the first equation,

`x+3(3.2)=6`
`x+9.6=6`
Subtract `9.6` from both sides.

`x=-3.6`

Answer 2

`x = -3.6 and y = 3.2`

Explanation:

`color(blue)(x)+3y =6" and "-6x+2y=28`

The system can be solved by using substitution.
(There is a single `x` so we can write `x` in terms of `y`)

`color(blue)(x = 6-3y)`

Substitute `color(blue)(6-3y)` for `color(blue)(x)` in the other equation:

`-6color(blue)(x)+2y=28" "rarr -6color(blue)((6-3y))+2y=28`

Now solve for `y`

`-36+18y +2y =28`

`20y = 64`

`y = 3.2" "larr` we have the value for `y`, find `x`

`x = 6-3(3.2)`

`x = 6-9.6`

`x =-3.6`