Question

How do you solve the system of equations algebraically `1/3x-3/2y=-4, 5x-4y=14`?

Answer 1

`y=4, x=6`

Explanation:

`1/3x-3/2y=-4` `color(white)(aa)` `-----`(1)
`5x-4y= 14` `color(white)(aaaaa)` `-----`(2)
`2x-9y=-24color(white)(aaa)` `-----(1) xx 6`--(3)
`10x-8y=28color(white)(aaa)` `-----(2) xx 2`--(4)
`10x-45y=-120color(white)(aaa)` `-----(3) xx 5`--(5)
`37y=148color(white)(aaa)` `-----(4) - (5)`
`y=148/37`
`y=4`
substitute y=4 in (2)

`5x-4(4)=14`

`5x-16=14`

`5x=30`

`x=6`

substitute y=4 and x=6 in (2)

`5(6)-4(4)=14`

`30-16=14`

`14=14`