How do you solve 3u + z = 15 and u + 2z = 10?

1 Answer
Sep 7, 2015

Answer:

#{(u=4), (z=3) :}#

Explanation:

Your system of equations looks like this

#{(3u+z = 15), (u + 2z = 10):}#

Multiply the first equation by #(-2)# to get

#{(3u+z = 15 | * (-2)), (u + 2z = 10):}#

#{(-6u-2z = -30), (u + 2z = 10):}#

Add these two equations to get one equation with one unknown, #u#

#-6u - color(red)(cancel(color(black)(2z))) + u + color(red)(cancel(color(black)(2z))) = -30 + 10#

#-5u = -20 implies u = ((-20))/((-5)) = color(green)(4)#

Now use this value of #u# in one of the wo original equations to find #z#

#4 + 2z = 10#

#2x = 6 implies z = 6/2 = color(green)(3)#