How do you solve the following system?: # x - 3y = 0 , 3x + y = 7 #

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Answer 1 · 2018-05-03T21:32:57

#x=21/10# and #y=7/10#

#x-3y=0#
#3x+y=7#

Let's solve for #x# in the first equation so we can use substitution

#x=3y#

Now plug that into the second equation

#3(3y)+y=7#

#9y+y=7#

#10y=7#

#y=7/10#

Plug that back into the first equation:

#x=3(7/10)#

#x=21/10#

#. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .#

To check our work, let's substitute #21/10# and #7/10# for #x# and #y# and solve. If we get the same answer as the equation, we are correct

#3x+y=7#

#3(21/10)+(7/10)# should equal #7#

#63/10+7/10#

#70/10#

#7# equals #7#

We were right!