How do you solve the following system?: #x +3y =8 , 6x +4y = -3#

1 Answer
May 12, 2018

Answer:

The values #x=-2 13/14# , #y=3 9/14# fulfills both equations.

Explanation:

It is always helpful to start with drawing the two equations as graphs in a diagram, not least as a check that our solution makes sense:

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We want to find a value of x and y which fulfill both equations at the same time, i.e. it must be on both lines f and g on the figure above.

As #x+3y=8#, it follows that
(1) #x=-3y+8#

Insert this value for x in the second equation. To make the solution simpler to follow I will write it as #-3=6x+4y#, that is:
#-3=6x+4y=6(-3y+8)+4y#
#-3=-18y+48+4y=-14y+48#

The last expression can be written as
#14y=48+3=51# or #y=51/14=3 9/14#

Insert this in expression (1):
#x=-3y+8=(-3)51/14+8=(-3*51*8*14)/14#
#x=(-153+112)/14=-41/14=-2 13/14#

Our solution, therefore, is
#x=-2 13/14# , #y=3 9/14#

If we convert these two values to decimal numbers, we see that it agrees with our graph.