Question

X² + y² = 34 = y = x+2 Show your working.

Answer 1

Answer:

$\left \{ {{y=5} \atop {x=3}} \right.$ or $\left \{ {{y=-3} \atop {x=-5}} \right.$

Step-by-step explanation:

Answer 2

Answer:

(- 5, - 3 ) , (3, 5 )

Step-by-step explanation:

x² + y² = 34 → (1)

y = x + 2 → (2)

substitute y = x + 2 into (1)

x² + (x + 2)² = 34

x² + x² + 4x + 4 = 34

2x² + 4x + 4 = 34 ( subtract 34 from both sides )

2x² + 4x - 30 = 0 ( divide through by 2 )

x² + 2x - 15 = 0 ← in standard form

(x + 5)(x - 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 3 = 0 ⇒ x = 3

substitute these values into (2) for corresponding values of y

x = - 5 : y = - 5 + 2 = - 3 ⇒ (- 5, - 3 )

x = 3 : y = 3 + 2 = 5 ⇒ (3, 5 )