# How do you solve y-2x=3 and 2x-3y=21 using substitution?

Mar 10, 2016

$x = - 7.5$
$y = - 12$

#### Explanation:

Start by writing one of these 2 equations in terms of $x$ or $y$ so that you have a substitutable form. Note that the substitutable means in the form of "$x =$" or "$y =$"

I'm going to start with getting $y - 2 x = 3$ in terms of $y$. I will call this equation 1. All we have to do here is add $2 x$ to each side,

$y - 2 x = 3$
Adding $2 x$ to each side:
$y = 3 + 2 x$

Now that we have the equation in terms of $y$, we can substitute this term (3+2x) into the other equation (equation 2).

$2 x - 3 y = 2 x - 3 \left(3 + 2 x\right) = 21$

Notice that now we have one equation with one variable. This means we can go ahead and solve for $x$

$2 x - 3 \left(3 + 2 x\right) = 2 x - 9 - 6 x = - 4 x - 9 = 21$
$- 4 x = 21 + 9 = 30$
$x = - 7.5$

Now that we have a value for $x$, we can substitute back into equation 1 to solve for $y$.

$y - 2 x = y - 2 \left(- 7.5\right) = y + 15 = 3$
Subtracting 15 from both sides and this solving for y,
$y = 3 - 15 = - 12$

Therefore,
$x = - 7.5$
$y = - 12$