Solve the simultaneous equations
5x-y=5
2y-x²=11
YOU MUST SHOW YOUR WORKING

(3, 10 ) and (7, 30 )

Step-by-step explanation:

Given the 2 equations

5x - y = 5 → (1)

2y - x² = 11 → (2)

Rearrange (1) expressing y in terms of x

y = 5x - 5 → (3)

Substitute y = 5x - 5 into (2)

2(5x - 5) - x² = 11

10x - 10 - x² = 11 ← rearrange into standard form

x² - 10x + 21 = 0 ← in standard form

(x - 3)(x - 7) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 7 = 0 ⇒ x = 7

Substitute these values into (3) for corresponding values of y

x = 3 → y = 5(3) - 5 = 15 - 5 = 10 ⇒ (3, 10 )

x = 7 → y = 5(7) - 5 = 35 - 5 = 30 ⇒ (7, 30 )

the distance from any point on the parabola to the focus is the exact same as the distance from that point to the directrix.

if you could provide answer choices that might allow me to answer the question easier if my above answer isn't an option! (: