Question

How do you solve the following system?: `y=2x + 3 , 9y = -3x - 9`

Answer 1

The solution for the system of equations is:
`color(blue)(x = -12/7`

`color(blue)(y = -3/7`

Explanation:

`color(blue)(y = 2x +3`..............equation `(1)`
`9y = -3x - 9`....equation `(2)`

Substituting equation `1` in equation `2:`

`9y = -3x - 9`

`9 xx (color(blue)( 2x +3)) = -3x - 9`

`18x + 27 = -3x - 9`

`18x + 3x = - 9 -27`

`21x = -36`

`x = -36/21`

`color(blue)(x = -12/7`

Finding `y` from equation `(1):`
`y = 2x +3`

`y = 2 xx (-12/7) +3`

`y = -24/7 +3`

`y = -24/7 +21/7`

`color(blue)(y = -3/7`