Solve the following system of equations and show all work. (10 points) y = 2x2 y = −3x −1

This system will have two real solutions.
I found them by setting each equation equal to each other and then setting it to zero (basically elimination method).
2x^2 = -3x-1
2x^2 + 3x + 1 = 0
You will get a new equation this way and it is a quadratic. Then you simply solve that equation by factoring to find your solutions.
2x^2 + 3x + 1 = 0
(2x + 1) (x+1) = 0
Then set each factor to zero to solve for x.
2x + 1 = 0
x = -1/2
and
x + 1 = 0
x = -1
I hope this makes sense and helps! If you have an questions then ask away. :)