Question

Select the correct answer.

Solve the system of equations.
y = x + 3
y = x^2 - 2x - 1

A. (1,4) and (-4,1)
B. (-1,4) and (4,1)
C. (-1,7 and (4,2)
D. (-1,2) and (4,7)

Answer 1

D. (-1, 2) and (4, 7).

Explanation:

Eliminating y:

x^2 - 2x - 1 = x + 3

x^2 - 3x - 4 = 0

(x - 4)(x + 1) = 0

x = -1, 4.

When x = -1, y = -1 + 3 = 2.

When x = 4, y = 4 + 3 = 7.

So the answer is (-1, 2) and (4, 7).

Answer 2

( 4,7) ( -1,2)

Explanation:

y = x + 3

y = x^2 - 2x - 1

Set the equations equal to each other

x + 3 = x^2 - 2x - 1

Subtract x from each side

3 = x^2 -3x -1

Subtract 3 from each side

0 = x^2 -3x -4

Factor

0 = ( x-4) ( x+1)

Using the zero product property

x-4 =0 x+1 =0

x = 4 x=-1

Find y for each x

x=4 y =x+3 y = 4+2 y=7

x = -1 y = x+3 y = -1+3 y = 2

( 4,7) ( -1,2)