Ume Find the coordinates of the points A and B where the line of x +2y = 10 intersects the curve of
2y^2– 7y + x = 0.

see explanation

Step-by-step explanation:

Given the 2 equations

x + 2y = 10 → (1)

2y² - 7y + x = 0 → (2)

Rearrange (1) expressing x in terms of y by subtracting 2y from both sides

x = 10 - 2y → (3)

Substitute x = 10 - 2y into (2)

2y² - 7y + 10 - 2y = 0

2y² - 9y + 10 = 0 ← in standard form

(y - 2)(2y - 5) = 0 ← in factored form

Equate each factor to zero and solve for y

y - 2 = 0 ⇒ y = 2

2y - 5 = 0 ⇒ 2y = 5 ⇒ y =

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

y = 2 → x = 10 - 4 = 6 ⇒ (6, 2 ) → B

y = → x = 10 - 5 = 5 ⇒ (5, ) → A

step-by-step explanation:

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