Question

How do you find the solution of the system of equations `3x + 6y = 18` and `2x + 5y = 20`?

Answer 1

You just need to isolate `x` or `y` in one of the equations and then substitute it in the other.

Let's isolate `x` in the first:

`x` = `18/3 - 6y/3`

`x` = `6 - 2y`

Now, we replace this found `x` in the second:

`2(6 - 2y) + 5y = 20`

`12 - 4y + 5y = 20`

`12 + y = 20`

`y = 8`

Now, you just replace this `y = 8` in the isolated `x` above:

`x = 6 - 2(8)`

`x = 6 - 16 = -10`

(There are other possible ways, for example using matrixes or subtracting one equation from another, but I would only recommend that in case you have MORE than two variables. The resolution I posted appears to be the simplest).