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

1 Answer
Sally
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−2x=3 in terms of y. I will call this equation 1. All we have to do here is add 2x to each side,

y−2x=3
Adding 2x to each side:
y=3+2x

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

2x−3y=2x−3(3+2x)=21

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

2x−3(3+2x)=2x−9−6x=−4x−9=21
Adding 9 to both sides,
−4x=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−2x=y−2(−7.5)=y+15=3
Subtracting 15 from both sides and this solving for y,
y=3−15=−12

Therefore,
x=−7.5
y=−12

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