Solve the following system of equations and show all work.

y = 2x2
y = –3x −1

We are given a system of equations.

Doing this, we get that the solutions of the system are:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

.

This polynomial has roots such that , given by the following formulas:

y = 2x³

y = –3x −1

Equaling them, we get:

Which is a quadratic equation with

We solve it to find the values of x.

Solutions of y:

For x = -1/2:

Thus, one of the solutions is:

For x = -1:

Thus, the other solution is: (-1,2).

Then, the two solutions are:

A similar question is given at link

(- 1, 2) and (- , )

Step-by-step explanation:

Given the 2 equations

y = 2x² → (1)

y = - 3x - 1 → (2)

Substitute y = 2x² into (2)

2x² = - 3x - 1 ( add 3x and 1 to both sides )

2x² + 3x + 1 = 0 ← in standard form

(2x + 1)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = -

x + 1 = 0 ⇒ x = - 1

Substitute these values into (2) for corresponding values of y

x = - 1 → y = - 3(- 1) - 1 = 3 - 1 = 2 ⇒ (- 1, 2 )

x = - → y = - 1 = ⇒ (- , )

dhdhth

step-by-step explanation: