Question

What are the solutions to the system of equations?
y = x² - 3
x - y = 1

Answer 1

Answer: x has no solutions, y has no solutions

Explanation:

y = x² - 3

x - y = 1

x - x² - 3 = 1

- x² - x - 3 = 1

- x² - x - 4 = 0

- x² - x - 16/4 = 0

- x² - x - 1/4 - 15/4 = 0

- (x² + x + 1/4) - 15/4 = 0

- (x+1/2)^2 - 15/4 = 0

- (x+1/2)^2 = 15/4

(x+1/2)^2 = -15/4 ==> x has no solutions, y has no solutions

any number to an even power, in this case to the power of 2, has to be positive, but -15/4 is negative.