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

2 Answers
Sep 25, 2015

y = 8 , x = -3

Explanation:

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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Sep 25, 2015

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

Explanation:

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)