Write an equivalent expression for each of the following
1 answer:
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Answer:
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