Question

How do you solve the system of equations: -3x-3y=3 and y=-5x-17?

Answer 1

When solved by substitution:

`x= -4`
`y= 3`

Explanation:

Let

`-3x - 3y = 3`

be eqn `(1)` and let

`y = -5x -17`

be eqn `(2)`. By means of substitution, we substitute eqn `(2)` into eqn `(1)` to find the unknown, `x`.

We arrive at:

`-3x -3(-5x - 17) = 3`

`-3x + 15x + 51 = 3`

`15x - 3x = 3 - 51`

`12x = -48`

`x = (-48)/12`

`x = -4`

We now have the value of `x`, hence we can substitute `x=-4` in eqn `(2)` to find the unknown `y`. By doing this, we arrive at:

`y = -5(-4) - 17`

`y = 20 - 17`

`y = 3`

Hence `x= -4 and y= 3`.

But to be sure, always double-check your work by replacing your values in the equations to see if they make the equations true.

`-3(-4) - 3(3) =3`
`12 - 9 = 3 ->` true

`3 = -5(-4) - 17`
`3 = 20 - 17 ->` true

The values of `x` and `y` make the equations true, hence `x=-4` and `y=3`.