Question

Solve the system of equations:

y = 2x
y= x2 - 3

ANSWERS:
a. (-1, -2) and (3, 6)
b. (-2, -4) and (2, 4)
c. (-1, 2) and (3, 2)
d. (-2, 1) and (2, 1)

Answer 1

`(-1,-2) \: \: \: \: \: and \: \: \: \: \: (3,6) \\ Answer: A`

Explanation:

`y = 2x \\ y = {x}^(2) - 3 \\ \\ 2x = {x}^(2) - 3 \\ {x}^(2) - 2x - 3 = 0 \\ (x + 1)(x - 3) = 0 \\ x + 1 = 0 \: \: \: \: \: or \: \: \: \: \: x - 3 = 0 \\ x = - 1 \: \: \: \: \: or \: \: \: \: \: x = 3`

When x = -1

Substitute x = -1 into y = 2x

y = 2(-1)

y = -2

( -1, -2)

When x = 3

Substitute x = 3 into y = 2x

y = 2(3)

y = 6

( 3, 6)