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)#