Help with systems of equations?

Question

y= x^2 + 2x - 8
y= 2x + 1

I need all the values of x and y. I would greatly appreciate it if you showed all the work! also, some explaining, if you dont mind...

Answer 1

Substitution method :

The equations are y = x² + 2x - 8 and y = 2x + 1.

To solve for x, substitute y = 2x + 1 in y = x² + 2x - 8.

2x + 1 = x² + 2x - 8

x² - 9 = 0

x² = 9

x² = (± 3)²

⇒ x = ± 3.

Substitute the values x = ± 3 in y = 2x + 1.

When x = - 3, y = 2(- 3) + 1 = - 6 + 1 = - 5.

When x = 3, y = 2(3) + 1 = 6 + 1 = 7.

The values of x and y : x = - 3 and y = - 5

                            x = 3 and y = 7.