Question

Use the elimination method to find all solutions of the system:

ſz? – 2y = 1
( :22 + 5y = 29
The two solutions of the system are:
(the one with < 0 is)

Answer 1

`x = 3` and
`y = 4`

Explanation:

Given

[Correct Question]

`x^2 - 2y = 1`

`x^2 + 5y = 29`

Required

Solve using elimination

First, we eliminate x.

Subtract equation (1) from (2)

`x^2 - x^2 + 5y - (-2y) = 29 - 1\\`

`5y - (-2y) = 28`

`5y +2y = 28`

`7y = 28`

Divide through ny 7

`y = 4`

Take
`x^2 - 2y = 1`

Make x^2 the subject

`x^2 = 1 + 2y`

Substitute 4 for y

`x^2 = 1 + 2*4`

`x^2 = 1 + 8`

`x^2 = 9`

Take square roots

`x = \sqrt 9`

`x = 3`