Question

Solve the system of equations.

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

Answer 1

To solve the system of equations y = x² - 2 and y = -2x + 1, you can use algebraic techniques to find the x-values that satisfy both equations and then substitute those x-values back into one of the equations to find the corresponding y-values. The solutions to the system are (-3, 7) and (1, -1).

Step-by-step explanation:

To solve the system of equations y = x² - 2 and y = -2x + 1, you can set the expressions for y equal to each other:

x² - 2 = -2x + 1

Now, you can rearrange the equation to get it in standard quadratic form:

x² + 2x - 3 = 0

Next, you can factor the quadratic equation:

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

Setting each factor equal to 0 gives you the x-values:

x + 3 = 0 -> x = -3

x - 1 = 0 -> x = 1

Therefore, the solutions to the system of equations are (-3, 7) and (1, -1).