Question

What are the solutions to the following system of equations?
y = x² + 7x-5
2x - y = -9

Answer 1

Explanation:

y = x² + 7x - 5 ............ (1)

2x - y = - 9 ................ (2)

(1) ------> (2)

2x - ( x² + 7x - 5 ) = - 9

- x² - 5x + 14 = 0 ........ (3)

- 1 × (3)

x² + 5x - 14 = 0

( x + 7 )( x - 2 ) = 0

`x_(1)` = - 7 and
`x_(2)` = 2

2( - 7) -
`y_(1)` = - 9 ⇒
`y_(1)` = - 5

2(2) -
`y_(2)` = - 9 ⇒
`y_(2)` = 13

The solutions of system are

( - 7, - 5 ) and ( 2, 13 )