Use substitution method to find all solutions of the system of equations
y=x^2
y=x+12

Question

Use substitution method to find all solutions of the system of equations
y=x^2
y=x+12

hero · Answer

y = y
x^2 = x + 12

anonymous · Answer

how do i get x by it's self if they are unlike terms?

hero · Answer

You don't. You create a quadratic equation instead:

x^2 - x - 12 = 0

Then you factor it.

hero · Answer

However, there is a series of steps you can perform to get x by itself. It requires completing the square.

hero · Answer

You could perform the following steps if you wanted to literally get x by itself:

x^2 = x + 12
x^2 - x = 12
x^2 - x + 1/4 = 12 + 1/4
(x - 1/2)^2 = 49/4
x - 1/2 = +/- 49/4
x = +/- 7/2 + 1/2

hero · Answer

Which simplifies to

x = 8/2 = 4
x = -6/2 = -3

anonymous · Answer

oh ok thank you I think I understand now

hero · Answer

You still have to find the y values. But not only that, you have to find the right solution pairs.

anonymous · Answer

for that do I just substitute the variables of x for x to find y?