Answer:
A(9, 2 ), B(13, 4 )
Step-by-step explanation:
Given the 2 equations
2y - x + 5 = 0 → (1)
(10 - x)² + (y - 5)² = 10 → (2)
Rearrange (1) expressing x in terms of y by adding x to both sides
x = 2y + 5 → (3)
Substitute x = 2y + 5 into (2)
(10 - (2y + 5))² + (y - 5)² = 10, that is
(10 - 2y - 5)² + (y - 5)² = 10
(5 - 2y)² + (y - 5)² = 10 ← expand the factors using FOIL
25 - 20y + 4y² + y² - 10y + 25 = 10
5y² - 30y + 50 = 10 ( subtract 10 from both sides )
5y² - 30y + 40 = 0 ( divide through by 5 )
y² - 6y + 8 = 0 ← in standard form
(y - 2)(y - 4) = 0 ← in factored form
Equate each factor to zero and solve for y
y - 2 = 0 ⇒ y = 2
y - 4 = 0 ⇒ y = 4
Substitute these values into (3) for corresponding values of x
y = 2 : x = 2(2) + 5 = 4 + 5 = 9 ⇒ (9, 2 )
y = 4 : x = 2(4) + 5 = 8 + 5 = 13 ⇒ (13, 4 )
Since we are not given the position of A or B in relation to each other then either of the points can represent A or B, that is
A(9, 2), B(13, 4)
OR
A(13, 4), B(9, 2)
