Question

How do you solve the system of equations `-2x + 2y = 32;2x + 3y = 18`?

Answer 1

`x=-6` and `y=10`

Explanation:

`-2x+2y=32`
`2x+3y=18`

Use the second equation to determine a value for `2x`.

`2x+3y=18`

Subtract `3y` from both sides.

`2x=18-3y`

In the first equation, substitute `2x` with `color(red)((18-3y))` keeping the negative sign in mind.

`-2x+2y=32`

`-color(red)((18-3y))+2y=32`

Open the brackets and simplify. The product of a negative and a positive is a negative; the product of two negatives is a positive.

`-color(red)(18+3y)+2y=32`

`-18+5y=32`

Add !18# to both sides.

`5y=50`

Divide both sides by `5`.

`y=10`

In the second equation, replace `y` with `color(blue)(10)`.

`2x+3y=18`

`2x+3(color(blue)(10))=18`

Open the brackets and simplify.

`2x+30=18`

Subtract `30` from each side.

`2x=-12`

Divide both sides by `2`.

`x=-6`