How do solve the following linear system?: #-4x + 4 = -4y, 7x + 6y + 11 = 0 #?

1 Answer
JMicheli
Jul 15, 2016

The solution is #(-5/13, 8/13)#

Explanation:

This problem makes things fairly easy for you by providing a clear definition of #y# in the first equation:

#-4x + 4 = -4y#
#x - 1 = y#

We can plug this into the other equation to solve for #x# and then use it to find #y#:
#7x + 6(x - 1) + 11 = 0#
#7x + 6x - 6 + 11 = 0#
#13x + 5 = 0#
#x = -5/13#

Then:
#-5/13 + 1 = y#
#y = 8/13#

So the solution is #(-5/13, 8/13)#

A little additional info on the problem in concluding. In case it is not clear, the solution takes the form of a point, #(x,y)#. This is because solving a system of equations is the same as finding the point(s) at which those lines (or curves) intersect.

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