Question

How do you solve the simultaneous equations `y - 3x = 2` and `3x + 2y = -14`?

Answer 1

The solution for the system of equations is:
`color(blue)(x=-2, y =-4`

Explanation:

`y−3x=2`
`y=color(blue)(2+3x` ..............equation `(1)`

`3x+2y=−14`.....equation `(2)`

Solving by substitution
Substituting equation `1` in equation `2`

`3x+2y=−14`

`3x+2(color(blue)(2+3x))=−14`

`3x+4+6x=−14`

`9x=−14-4`

`9x=-18`
`color(blue)(x=-2`

Substituting `x` in equation `1` to find `y`
`y=2+3x`
`y=2+3(-2)`
`y=2-6`
`color(blue)(y=-4`