The first three steps in determining the solution set of the system of equations algebraically are shown.

y = x2 − x − 3
y = −3x + 5

what are the solutions of this system of equations?

(−2, −1) and (4, 17)
(−2, 11) and (4, −7)
(2, −1) and (−4, 17)
(2, 11) and (−4, −7)

In order to solve the system of equations algebraically you have to follow those steps

we have

------> equation A

-------> equation B

Step 1

Equate the equation A and equation B

Step 2

Convert the quadratic equation in factored form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side.

Rewrite as perfect squares

Square root both sides

Step 3

Find the values of y

Substitute the value of x in the equation B

For

For

therefore

the answer is

and