How do you determine the solution in terms of a system of linear equations for 5x+7y=41 and 3x+7y=47?

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Answer 1 · 2015-09-25T12:42:35

#y = 8 , x = -3#

#5x+7y=41 ,3x+7y=47#

There are numerous ways But i shall do the easiest one

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Now the Final part;

Plug the value in ---1

#7y = 41 - 5(-3)#

#7y = 41 + 15#

#7y = 56#

#y = 8#

Now there is the graphical and mechanical way of solving this

Mechanical(Boring ,No fun);

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Answer 2 · 2015-09-25T12:54:45

You should write a variable in terms of the other variable.

#5x + 7y = 41# so we can say that #5x = 41 - 7y#, so

#x = (41 - 7y)/5#

In the other equation, we have

#3x + 7y = 47#

We know that we can write #(41 - 7y)/5# instead of #x#. So we get

#3 * (41 - 7y)/5 + 7y = 47#

In order to solve this equation, you need to expand it;

#(123 - 21y)/5 + 7y = 47#

#123 - 21y + 35y = 235#

#14y = 112 implies y=8#

Then you can easily find #x# by writing #8# insted of #y# in one of the equations:

#5x + 7y = 41#

#5x + 56 = 41#

#5x = -15 implies x = -3#

#3x + 7y = 47#

#3x + 56 = 47#

#3x = -9 implies x = -3#

So the result is; #( -3 , 8)#