GRAPHS, FUR1 2002 VCAA 4 MC

For the pair of simultaneous equations

`4x = 7 - y`

`5x + 7y = 3`

the solution is

A. `x = –2, y = –1`

B. `x = –2, y = 1`

C. `x = 1, y = 3`

D. `x = –1, y = 2`

E. `x = 2, y = –1`

Show Answers Only

`E`

Show Worked Solution

`4x`	`= 7 − y`
`4x + y`	`= 7`
`7(4x + y)`	`= 7(7)`
`28x + 7y`	`= 49 \ \ \ …\ text{(i)}`

`5x + 7y“= 3 \ \ \ \ …\ text{(ii)}`

`text{(i) − (ii)}`

`23x`	`= 46`
`x`	`= 2`

`text(Sub)\ x = 2\ text{into (ii)}`

`5(2) + 7y`	`= 3`
`10 + 7y`	`= 3`
`7y`	`= text(−7)`
`y`	`= text(−1)`

`:.\ x = 2, y = text(−1)`

`=> E`