Answer:
(- 2, - 1 ), (2, 1 )
Step-by-step explanation:
Given the 2 equations
x - 2y = 0 → (1)
x² - y² = 3 → (2)
Rearrange (1) expressing x in terms of y by adding 2y to both sides
x = 2y → (3)
Substitute x = 2y into (2)
(2y)² - y² = 3, that is
4y² - y² = 3
3y² = 3 ( divide both sides by 3 )
y² = 1 ( take the square root of both sides )
y = ± [tex]\sqrt{1}[/tex] = ± 1
Substitute these values into (3) for corresponding values of x
y = - 1 ⇒ x = 2(- 1) = - 2 ⇒ (- 2, - 1 )
y = 1 ⇒ x = 2(1) = 2 ⇒ (2, 1 )
