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

May 13, 2015

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:

$x$ = $\frac{18}{3} - 6 \frac{y}{3}$

$x$ = $6 - 2 y$

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

$2 \left(6 - 2 y\right) + 5 y = 20$

$12 - 4 y + 5 y = 20$

$12 + y = 20$

$y = 8$

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

$x = 6 - 2 \left(8\right)$

$x = 6 - 16 = - 10$

(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).