Question

How do you solve the system of equations `3x - 3y = 7` and `2x + y = 12`?

Answer 1

`x=43/9`, `y=22/9`

Explanation:

Alright, there are two ways of approaching your example:

1. Find the value of `x` in terms of `y`;

`3x-3y=7`
`x = (3y+7)/3`

Then, substitute `x` with that value in the other equation;

`2((3y+7)/3)+y=12`

Then solve for y.

`(6y+14)/3=12-y`
`6y+14=36-3y`
`9y =22`
`y=22/9`

Once `y` is found, you can substitute its value in its position and find `x`.

`2x+(22/9)=12`
`2x=86/9`
`x=43/9`

You could want to find the value of `x` first, then go for the `y`, it's completely up to you.

1. Make the coefficients of either the `y`'s or `x`'s the same number in both the equations by multiplying them by factors.

In this case I can multiple the second equation by `-3` in order to make the `y`'s coefficient `-3` in both of the equations.
You could also for example multiply the first equation by `2` then multiply the second equation by `3`, thus making the `x`'s the same.

`-3*(2x+y)=-3*(12)`
`-6x-3y=-36`

Now, you subtract one equation from the other. Since you make one of the variables the same, they will cancel out to give `0`;

`3x-(-6x)-3y-(-3y)=7-(-36)`
`9x=43`
`x=43/9`

You now substitute `43/9` into either of the original equations to find that `y=22/9`.