How do you solve the following system using substitution?: #4x + 5y = 6, y = 2x - 10#

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Answer 1 · 2015-10-22T10:44:23

#x=4#, #y=-2#.

From the second equation, we know that #y=2x-10#. So we can susbtitute every occurrence of #y# with #2x-10# in the first equation:

#4x+5color(green)(y)=6 -> 4x+5color(green)((2x-10))=6#.

Expanding, we have #4x+10x-50=6#. Isolating the #x# term, we have

#14x = 56#, which we solve for #x# finding #x= 56/14=4#.

Once we know the value of #x#, we obtain #y# by substituing in the second equation (for example):

#y=2x-10 -> y=2*4-10 = -2#.

Note that we could have chosen the first equation:

#4x+5y=6 -> 4*4+5y=6 -> 5y=-10 -> y=-2#.