Question

Y=
`4x^(2)`+3x+4
y=5x+4

Answer 1

(0, 4 ) and (
`(1)/(2)`,
`(13)/(2)` )

Explanation:

Given the2 equations

y = 4x² + 3x + 4 → (1)

y = 5x + 4 → (2)

Substitute y = 4x² + 3x + 4 into (2)

4x² + 3x + 4 = 5x + 4 ( subtract 5x + 4 from both sides )

4x² - 2x = 0 ← factor out 2x from each term

2x(2x - 1) = 0

Equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

2x - 1 = 0 ⇒ 2x = 1 ⇒ x =
`(1)/(2)`

Substitute these values into (2) for corresponding values of y

x = 0 : y = 5(0) + 4 = 0 + 4 = 4 ⇒ (0, 4 )

x =
`(1)/(2)` : y =
`(5)/(2)` + 4 =
`(13)/(2)` ⇒ (
`(1)/(2)`,
`(13)/(2)` )