Question

How do you solve the system of equations and enter the solution as an ordered pair 7x - 5y = 31 and 4x - 7y = -3?

Answer 1

`x = 8` and `y = 5`

Explanation:

`7x - 5y = 31 color(white)(...)……(1)`
`4x - 7y = -3 color(white)(...) …….(2)`

Multiply first equation by `7` and second equation by `5`
Now, we have

`49x - 35y = 217`
`20x - 35y = -15`

Subtract second equation from first one

`(49x - 35y) - (20x - 35y) = 217 - (-15)`

`49x - 35y - 20x + 35y = 217 + 15`

`49x - 20x = 232`

`29x = 232`

`x = 232/29`

`color(blue)(x = 8)`

Substitute `x = 8` in equation `(1)`

`7(8) - 5y = 31`

`56 - 5y = 31`

`5y = 56 - 31`

`y = (56 - 31)/5`

`color(blue)(y = 5)`