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

1 Answer
Jun 8, 2015

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)