Question

Solve this system? `-6=3x-6y` and `4x=4+5y`

Answer 1

`x=6, y=4`

Explanation:

We have:

`-6=3x-6y` and `4x=4+5y`. Two equations with 2 unknowns!

There are a number of ways to approach this. I'm going to take the first equation, solve for x, and substitute into the second equation. The reason I'm doing it this way is that I can see that all the terms have a multiple of 3 in them and so will be easier to work with that way then other methods.

`-6=3x-6y` and now divide by 3 on both sides:

`-2=x-2y` and now solve for x:

`x=2y-2`

We can now substitute in:

`4x=4+5y`

`4(2y-2)=4+5y` and now solve for `y`:

`8y-8=4+5y`

`3y=12`

`y=4`

And now we can substitute this back in:

`x=2y-2`

`x=2(4)-2`

`x=6`