How do you solve the following system: #2x-y/2=4, 5x+2y=20 #?

1 Answer
Ben
Mar 23, 2018

Use linear algebra to solve for x, and then plug the solution back in to solve for y. You will find that #x=36/13# and #y=40/13#.

Explanation:

Let's align the equations, first and foremost:

#2x-y/2=4#
#5x+2y=20#

To eliminate y, we'll multiply the entire top equation by 4, which will make that #-y/2# into #-2y#. We'll then add the two equations together and get a system where it's only x and constants:

#(2x-y/2=4)xx4 rArr 8x-2y=16#

# (8x-2y=16)#
#ul(+(5x+2y=20))#
#13x=36#

#color(red)(x=36/13#

Now, let's plug it back into one of the equations to solve for y:

#5x+2y=20 rArr 5(36/13)+2y=20#

#(5/2)(36/13)+y=10 rArr (5*18)/13+y=10#

#y=10-90/13 rArr y=130/13-90/13=(130-90)/13#

#color(blue)(y=40/13)#

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