Question

If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the second equation is substituted into the first equation.

3x + 2y = -21
x - 3y = 4
Choose one answer. a. 3(3y + 4) + 2y = -21
b. 3(-3y + 4) + 2y = -21
c. 3x + 2(3y + 4) = -21
d. 3x + 2(-3y + 4) = -21
.

Answer 1

So what we want to do is choose one of the two equations and then isolate one of the variables in that equation. Basically, get x or y by itself on one side of the equal sign. Given your two equations, it looks easiest to do this with the second one. So for the second one, we can get x all by itself by adding 3y to both sides. That will give us this:

x = 4 + 3y

Now we take this new found value of x and plug it into the other equation, replacing x with this value. Doing that looks like this:

3(4+3y) + 2y = -21.

The x was completely replaced with the 4+3y value and put in parenthesis because we want this to be multiplication. So now I need to multiply this out and solve for y. This gives me:

12 + 9y + 2y = -21
12 + 11y = -21
11y = -33
y = -3

So this is how you would go about solving for one of the variables. Now that I know what y is, I can substitute this into either equation and solve for x. The second one looks like the easiest to do this with, so Ill replace y with -3 in the second one. That'll give me:

x-3(-3) = 4
x + 9 = 4
x = -5

So that would be our x and y value and the point of intersection for this system, (-5,-3)