Question

How do you solve the system `4x - y = 5` and `x + y = 10`?

Answer 1

`x+y=10`
Thus : `color(blue)(x=10-y` ( we substract `color(red)y` on each side )

We can now replace it in the first equation :

`4color(blue)x-y=5`
`4*color(blue)((10-y))-y=5`
`40-4y-y=5`
`40-5y=5`
`40=5+5y` ( we add `5y` on each side )
`40-5=5y` ( we substract `5` on each side )
`35=5y`
`color(red)(y=7` ( we divide by `5` on each side )

We can now calculate `color(blue)x` with `color(red)y` :

`color(blue)x=10-color(red)y`
`color(blue)x=10-color(red)7`
`color(blue)(x=3)`