Question

Solve the system of equations.y = x2 - 2y = -2x + 1A. (-3,7) and (-1,3)B. (-3,7) and (1, -1)C. (1.-1) and (3,-5)D. (-1,3) and (3, -5)

Answer 1

Option B is correct.

the solutions to the system of equations include

(-3, 7) and (1, -1)

Explanation

The question is to solve the system of equations

y = x² - 2 ..... equation 1

y = -2x + 1 ..... equation 2

To solve this, we can just equate the expression given for y in equation 1 to the expression given for y in equation 2.

y = x² - 2

y = -2x + 1

Since

y = y

x² - 2 = -2x + 1

x² + 2x - 2 - 1 = 0

x² + 2x - 3 = 0

This gives a quadratic equation which we will now solve

x² + 2x - 3 = 0

x² + 3x - x - 3 = 0

x (x + 3) - 1 (x + 3) = 0

(x - 1) (x + 3) = 0

So,

x - 1 = 0 or x + 3 = 0

x = 1 or x = -3

If x = 1,

y = x² - 2

= 1² - 2

= 1 - 2

= -1

x = 1, y = -1

If x = -3

y = x² - 2

= (-3)² - 2

= 9 - 2

= 7

x = -3, y = 7

So, the solutions to the system of equations include

x = -3, y = 7, that is, (-3, 7)

And

x = 1, y = -1, that is, (1, -1)

Hope this Helps!!!