the solutions are (1, - 5 ) and (5, - 1 )
y² - 26 = - x² → (1)
x - y = 6 → (2)
rearrange (2) in terms of x or y, that is
x = 6 + y
substitute this value into equation (1)
y² - 26 = - (6 + y )² ← distribute and rearrange into standard form
y² - 26 = - 36 - 12y - y²
2y² + 12y + 10 = 0 ← in standard quadratic form
divide through by 2
y² + 6y + 5 = 0
(y + 5)(y + 1 ) = 0 ← in factored form
y + 5 = 0 ⇒ y = - 5
y + 1 = 0 ⇒ y = - 1
substitute these values into x = 6 + y for corresponding values of x
y = - 5 : x = 6 - 5 = 1 ⇒ (1, - 5 ) is a solution
y = - 1 : x = 6 - 1 = 5 ⇒ (5, - 1 ) is a solution
