Question

How do you solve the following system?: `-2x -3y =15, -3x +y = -17`

Answer 1

The solution for the system of equations is:

`x = 36/11`

`y = -79/ 11`

Explanation:

`-2x color(blue)(- 3y) = 15`..................equation `(1)`

`-3x + y = -17`, multiplying by `3`
`-9x + color(blue)(3y) = -51`.............equation `(2)`

Solving by elimination:

Adding both the equations eliminates `color(blue)(3y):`

`-2x cancelcolor(blue)(- 3y) = 15`
`-9x + cancelcolor(blue)(3y) = -51`

`-11x = -36`

`x = (-36)/ (-11)`

`x = 36/11`

Finding `y` from equation `1`:
`-2x - 3y = 15`

`-2x - 15 = 3y`

`-2 * (36/11) - 15 = 3y`

`-72/11 - 15 = 3y`

`-72/11 - 165/11 = 3y`

`-237/ 11 = 3y`

`-237/ (11 * 3) = y`

`y = -79/ 11`