Answer:
(0, -2) and (3, 1)
Explanation:
y = x - 2, y = (x - 1)² - 3
To solve this problem, we need to find when the x and ys in both equations are equal.
So,
y = x - 2 = y = (x - 1)² - 3
x - 2 = (x - 1)² - 3
Simplify right side.
x - 2 = x² - 2x - 2
Subtract both sides by (x² - 2x - 2)
x - 2 - (x² - 2x - 2) = 0
Simplify.
-x² + 3x = 0
Factor x.
x (-x + 3) = 0
Because the only way to get a product of 0 is to multiply a number by 0, either x = 0 or (-x + 3) = 0 (x would be 3 in this equation)
So, x = 0 or x = 3
Now, to find y, plug x = 0 x = 3 into one of the equations.
When x = 3, y = x - 2 = 3 - 2 = 1
When x = 0, y = x - 2 = 0 - 2 = -2
Just in case, let's check these values.
Put x = 0 and y = -2 into y = (x - 1)² - 3
-2 = (0 - 1)² - 3 = (-1)² - 3 = 1 - 3 = -2
So, x = 0 and y = -2 is correct.
Put x = 3 and y = 1 into y = (x - 1)² - 3
1 = (3 - 1)² - 3 = 2² - 3 = 4 - 3 = 1
So, x = 3, y = 1 is correct.
Thus, the answers are
(0, -2) and (3, 1)
I hope this helps! Feel free to ask any questions!