Question

How do you solve the following system: #-29=5y-3x, 4x-5y= -1 #?

Answer 1

Solve the former one first
`-29=5y-3x`
Solve for `y`
Transfer `3x`
`3x-29=5y`
You can also transfer the `5` in `5y` but that would be stupid considering that the next equation wants `5y`
The latter equation
`4x-5y=-1`
Put the value of `5y`
`4x-(3x-29)=-1`
Which gives us
`4x-3x+29=-1`
Solve
`x+29=-1`
Transfer the `-1`
`x+29+1=0`
`x+30=0`
Which gives
`x=-30`
`5y=3x-29`
Put value of `x`
`5y=3xx(-30)-29`
Solve
`5y=-90-29`
Solve
`5y=-119`
Transfer `5`
`y=-119/5`
Or...
`y=-23.8`