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 = ⇒ (- , )

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98