Question

How do you solve the system of equations `6x - 3y = 12` and `- 5x + 3y = - 5`?

Answer 1

`x=7, y=10`

Explanation:

We have that:

`-5x+3y=-5`
`6x-3y=12`

We can easily solve by eliminating the `y` value. Add both equations together to get:

`(-5x+3y)+(6x-3y)=-5+12`

Simplifying leaves us with:

`x=7`

We can now substitute our value of `x` back into either of these equation to get `y`. We will chose the top one:

`-5x+3y=-5`

`x=7-> -5(7)+3y=-5`

`-35+3y=-5`

So:
`3y=30-> y=10`

Hence `x=7, y=10`

We can check the solution by substituting into the other equation, so:

`6x-3y=12`
`x=7, y=10->6(7)-3(10)=42-30=12`

As expected.