Question

Solve by the substitution method:

7x + 9y = -12

-3x + y = 10

Answer 1

The substitution method simply means to set one variable equal to an equation, then plug that equation into the other in place of your variable.

Answer 2

The easiest one to do first is the lower, what would y equal in that instance?

Answer 3

13?

Answer 4

You would subtract 3x from both sides to give you y=10+3x

Answer 5

Now that you know what y equals, plug that value (10+3x) into the first equation in place of y.

Answer 6

y = 13 x = 3??

Answer 7

No, your lower equation is -3x+y=10, so solving for y you get y=10+3x, you cannot solve any further as you do not know what 'x' or 'y' is. Using substitution allows you to take your new equivalent for 'y' and place it in the upper equation so that you can solve for x.

Answer 8

So you start out with 7x+9y=-12 and replace the 'y' with it's equivalent value to give you 7x+9(10+3x)=-12 and then solve for x

Answer 9

ok x = 3 in that case

Answer 10

Close, you forgot a sign, it will be -3.
\[7x+9(10+3x)=-12 \rightarrow 7x + 90 + 27x=-12 \rightarrow 34x=-102 \rightarrow x=\frac{-102}{34}=-3\]
Now take that value for x and plug it back into the lower equation, -3x+y=10

Answer 11

Y = 1?

Answer 12

Correct. Now if you plug your x=-3 and y=1 values into those two equations you will see that they both work out.

Answer 13

Ok great! Thanks so much :)

Answer 14

You're welcome