Question

How do you solve the system of equations `-8x + 4y = - 12` and `- x - y = - 3`?

Answer 1

`x=2`
`y=1`

Explanation:

Equation 1: `-8x+4y=-12`
Equation 2: `-x-y=-3`

Because its easier to work with positive values, I'm going to multiple both sides of equation 2 by -1.

`x+y=3`

I'm going to make `y` the subject of equation 2 by subtracting `x` from both sides so I can substitute it into equation 1.

`y=3-x`

Substitute this value for `y` into equation 1.

`-8x+4(3-x)=-12`

Solve for `x`. Start by expanding the parenthesis.

`-8x+12-4x=-12`

Then combine the like terms `-8x` and `-4x`.

`-12x+12=-12`

Subtract 12 from both sides of the equation.

`-12x=-24`

Multiply both sides of the equation by -1 to make them positive.

`12x=24`

Divide both sides of the equation by 12 to leave `x`.

`x=2`

Now we've found `x` and need to find `y`. Remember earlier how we found that `y=3-x`? All we have to do is substitute our value for `x` into this equation to find `y`.

`y=3-(2)`
`y=1`