Question

How do you solve the following system: #9x - 3y = -30, -5x + 3y= 6 #?

Answer 1

The solution for the system of equations is

`color(blue)(x=-6,y=-8`

Explanation:

`9xcolor(blue)(-3y)=-30`.....equation `(1)`

`-5x+color( blue)(3y)=6`.........equation `(2)`

Solving by elimination.

Adding the two equations results in elimination of `color(blue)(3y`

`9x cancelcolor(blue)(-3y)=-30`

`-5x+cancelcolor( blue)(3y)=6`

`4x=-24`

`x=-24/4`

`color(blue)(x=-6`

Finding `y` by substituting `x` in equation `1`

`9x-3y=-30`

`9 xx (-6)-3y=-30`

`-54-3y=-30`

`-24 = 3y`

`y = (-24)/3`

`color(blue)(y=-8`