Question

Solve the following system of equations and show all work.
y = 2x2
y =-3x -1

Answer 1

Explanation:

Start by substituting the first equation into the second equation to eliminate y:

2x^2 = -3x - 1

Move all terms to one side:

2x^2 + 3x + 1 = 0

Factor the quadratic equation:

(2x + 1)(x + 1) = 0

Solve for x by setting each factor to zero:

2x + 1 = 0 or x + 1 = 0

x = -1/2 or x = -1

Plug in the values of x to find the corresponding values of y:

For x = -1/2:

y = 2(-1/2)^2 = 1/2

For x = -1:

y = 2(-1)^2 = 2

The solutions to the system are (-1/2, 1/2) and (-1, 2).