Question

How do you solve the following system: `3x-y=12, 4x-y=6`?

Answer 1

I'll solve this systems of equations for you by substitution

Explanation:

We must first isolate a variable.

`3x - y = 12`

`-y = 12 - 3x`

`y = -12 + 3x`

Now, knowing y, we can substitute for y in the other equation.

`4x - (-12 + 3x) = 6`

`4x + 12 - 3x = 6`

`x = -6`

`3(-6) - y = 12`

`-18 - y = 12`

`-y = 30`

`y = -30`

The solution set is `{-6, -30}`. Note that the solution set must always be of the form `{x, y}`, as noted in graphing. Eg. the point (8,5) is 8 on the x axis and 5 on the y axis graph.

Hopefully this helps!