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)

( 4,7)    ( -1,2)

Step-by-step 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)

D.  (-1, 2) and (4, 7).

Step-by-step 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).

m∠5 + m∠3 = m∠1   is true.

m∠5 + m∠6 = 180 is true

m∠2 +m∠3 = m∠6   is true

m∠2 +m∠3 +m∠5 = 180   is true

step-by-step explanation: