Question

How do you solve `-x + y = 12` and `x + 2y = 3`?

Answer 1

`{(x=-7), (y=5) :}`

Explanation:

All you really ahve to do to solve this system of equations is add the left side and the right side of the equations separately to eliminate the variable `x`.

`-color(red)(cancel(color(black)(x))) + y + color(red)(cancel(color(black)(x))) + 2y = 12 + 3`

`3y = 15`

To get the value of `y`, simply divide both sides of the equation by `2` to get

`(color(red)(cancel(color(black)(3))) * y)/color(red)(cancel(color(black)(3))) = 15/3 => y = color(green)(5)`

Now use this value of `y` in one of the two equations to get the value of `x`.

`x + 2 * 5 = 3`

`x + 10 = 3`

Add `-10` to both sides of the equation

`x + color(red)(cancel(color(black)(10))) - color(red)(cancel(color(black)(10))) = 3-10 => y = color(green)(-7)`

Answer 2

I found:
`x=-7`
`y=5`

Explanation:

You can add the two equations (in column):
`{-x+y=12`
`{x+2y=3`
`color(red)(0+3y=15)`
so `y=15/3=5`
substitute this value into the first equatiom:
`-x+5=12`
`-x=7`
`x=-7`