Question

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

Answer 1

Substitution/Elimination/Graphing Method

Explanation:

Using the substitution method, starting with the first equation:

`9y = -3x-9`

`9y+9 = -3x`

`(9y)/-3+9/-3 = (-3x)/-3`

`x = -3y -3`

Substituting `(x=-3y-3)` into the second equation to find `y`:

`5x+3y = -3`

`5(-3y-3) + 3y=-3`

`-15y-15 + 3y=-3`

`-12y=12`

`y=-1`

Now substituting `(y=-1)` into second equation to find `x`:

`5x+3y = -3`

`5x+3(-1)=-3`

`5x-3 = -3`

`5x= 0`

`x =0`

Test `(x=0, y=-1)` in other equation to validate

`9y = -3x-9`

`9(-1) = -3(0)-9`

`-9 = -9`,