Question

The question is the image

Answer 1

(- 4, 16 ) , (
`(1)/(2)`,
`(1)/(4)` )

Explanation:

y = x² → (1)

7x + 2y = 4 → (2)

substitute y = x² into (2)

7x + 2x² = 4 ( subtract 4 from both sides )

2x² + 7x - 4 = 0 ← in standard form

(x + 4)(2x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

2x - 1 = 0 ⇒ 2x = 1 ⇒ x =
`(1)/(2)`

substitute these values into (1) for corresponding values of y

x = - 4 : y = (- 4)² = 16 ⇒ (- 4, 16 )

x =
`(1)/(2)` : y = (
`(1)/(2)` )² =
`(1)/(4)` ⇒ (
`(1)/(2)` ,
`(1)/(4)` )