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How do you solve the following linear system #2x-y=4, x+3y=1? #?

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Ben Share
Jun 22, 2018

Answer:

Solve for one term with respect to another, then solve for the second term, then back-solve for the first. You will find that #x=13/7# and #y=-2/7#

Explanation:

First, we'll want to solve for either #x# in terms of #y# or vice versa. For the sake of argument, we'll sove for #x# in terms of #y# using the second expression:

#x+3y=1#

#rArrcolor(blue)(x=1-3y)#

Now, we take that solution for #x# and substitute it in, in expression 1:

#2color(blue)(x)-y=4#

#2color(blue)((1-3y))-y=4#

#2-6y-y=4#

#2-7y=4#

#-7y=2#

#color(green)(y=-2/7)#

We now have a solution for #y#. We can then plug it into either expression to solve for #x#:

#x+3color(green)(y)=1#

#x+3color(green)((-2/7))=1#

#x-6/7=1#

#x=1+6/7#

#color(green)(x=13/7)#

And now we have our solution:

#x=13/7#, #y=-2/7#

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