Question

How do you solve the following system: #4x-2y=4 , 4x-5y-23=0 #?

Answer 1

`x = -13/6 and y = -19/3`

Explanation:

Write both equations with `4x` as the subject.

`4x = 2y+4" and "4x = 5y +23`

`color(white)(xxxxxxxx)4x = 4x`

`color(white)(xxxxx)5y +23 = 2y+4`

`color(white)(xxxxx)5y -2y = 4-23`

`color(white)(xxxxxxxx)3y = -19`

`color(white)(xxxxxxxxx)y = -19/3`
`4x= (2y+4)`

`x = (2y+4)/4`

`x = (2((-19)/3) +4)div 4`

`x = -13/6`

Check:

`4x = 5y+23`

`4xx(-13)/6 = 5((-19)/3)+23`

`-26/3 = -26/3`