Answer:
(1, - 5 ) and (5, - 1 )
Step-by-step explanation:
Given the 2 equations
x² + y² = 26 → (1)
x - y = 6 → (2)
Rearrange (2) making x the subject by adding y to both sides
x = 6 + y → (3)
Substitute x = 6 + y into (1)
(6 +y )² + y² = 26 ← expand (6 + y)² and simplify left side
36 + 12y + y² + y² = 26
2y² + 12y + 36 = 26 ( subtract 26 from both sides )
2y² + 12y + 10 = 0 ( divide through by 2 )
y² + 6y + 5 = 0 ← in standard form
(y + 5)(y + 1) = 0 ← in factored form
Equate each factor to zero and solve for y
y + 5 = 0 ⇒ y = - 5
y + 1 = 0 ⇒ y = - 1
Substitute these values into (3) for corresponding values of x
x = - 5 : x = 6 - 5 = 1 ⇒ (1, - 5 )
x = - 1 : x = 6 - 1 = 5 ⇒ (5, - 1 )
