How do you solve the system of equations #6u + v = 18# and #5u + 2v = 22#?

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Answer 1 · 2016-12-20T13:05:05

#u = 2# and #v = 6#

Step 1) Solve the first equation for #v#:

#6u - color(red)(6u) + v = 18 - color(red)(6u)#

#0 + v = 18 - 6u#

#v = 18 - 6u#

Step 2) Substitute #18 - 6u# for #v# in the second equation and solve for #u#:

#5u + 2(color(red)(18 - 6u)) = 22#

#5u + 36 - 12u = 22#

#5u + 36 - color(red)(36) - 12u = 22 - color(red)(36)#

#5u + 0 - 12u = -14#

#5u - 12u = -14#

#(5 - 12)u = -14#

#-7u = -14#

#(-7u)/color(red)(-7) = (-14)/color(red)(-7) #

#(color(red)(cancel(color(black)(-7)))u)/color(red)(cancel(color(black)(-7))) = 2#

#u = 2#

Step 3) Substitute #2# for #u# in the solution to the first equation in Step 1 and calculate #v#:

#v = 18 - (6*2)#

#v = 18 - 12#

#v = 6#