Question

Solve the following system of equations and show all work.

y = 2x^2
y = –3x −1

Answer 1

The two equations equal the same thing (y) so you can set them equal to each other to solve for x

Answer 2

How? I tried to but I got stuck.

Answer 3

This is the transitive property/ substitution.
If A = B
A = C, then
B = C.
You can apply this to your problem.

Answer 4

You should get 2x^2 + 3x + 1 = 0

Answer 5

I got to that part. I just don't know how to go further.

Answer 6

Now it just comes down to factoring.
You need two numbers that add to the coefficient of the x term and multiply to the product of the constant and coefficient of x^2.

So two numbers that add to 3 and multiply to 2.

Answer 7

So 2 and 1? (2x+1)(x+1)

Answer 8

Yes that's the correct factorization.
(2x+1)(x+1) = 0

Now notice you have (2x+1) multiplied by (x+1) equals 0, so either 2x+1 or x+1 = 0 by the zero product property.
So,
2x+1 = 0 or
x + 1 = 0