Question

Solve these two equations simultaneously
7x+y = 1 and 2x² - y = 3

Answer 1

(- 4, 29 ) and (
`(1)/(2)`, -
`(5)/(2)` )

Explanation:

7x + y = 1 ( subtract 7x from both sides )

y = 1 - 7x → (1)

2x² - y = 3 → (2)

substitute y = 1 - 7x into (2)

2x² - (1 - 7x) = 3

2x² - 1 + 7x = 3

2x² + 7x - 1 = 3 ( subtract 3 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 = 1 - 7(- 4) = 1 + 28 = 29 ⇒ (- 4, 29 )

x =
`(1)/(2)` : y = 1 - 7(
`(1)/(2)` ) = 1 -
`(7)/(2)` = -
`(5)/(2)` ⇒ (
`(1)/(2)`, -
`(5)/(2)` )