Select the correct answer. What is the solution set of x2 + y2 = 26 and x − y = 6?

(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 )