How do you solve #2x+2y=14# and #2x-y=5# using substitution?

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Answer 1 · 2016-04-08T09:18:15

#x = 4, y = 3#

First you want to find a definition for either #x# or #y# in terms of the other, using the second equation.

#2x - y = 5#
#2x = y + 5#
#y = 2x - 5#

Now you can substitute this into the first equation.

#2x + 2y = 14#
#2x + 2(2x - 5) = 14#
#6x - 10 = 14#
#6x = 24#
#x = 4#

With this value, substitute into anything and it should give you #y#. Lets use the direct equation for #y# we found.

#y = 2x - 5#
#y = 2 * 4 - 5#
#y = 3#

You can substitute these values into any of the equations and they should work, if they are correct.