Lauren J.

asked • 04/12/17

solve systems of equations

use the substitution method or the elimination method to solve the following system. 
5x-30y=15
-7x+42y=-21

2 Answers By Expert Tutors

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Kenneth S. answered • 04/12/17

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Notice that you can divide every term of the first equation by 5 and thus discover that x = 3 +6y.
 
Also, you can now divide the second equation by 7 (or -7) everywhere to simplify it, and then substitute for x, thus leading to y = some particular number.  Then calculate x per my first paragraph.
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Lauren J.

Every time that I do it I get no solution though
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04/12/17

Mark M.

Follow Kenneth's process. You arrive at to identical equations. All solutions of one are solutions of the other.
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04/12/17

Kenneth S.

That's because both equations boil down to the same ONE EQUATION, so the solution is one line, containing infinitely many points.
 
For a system of two linear equations, there are three possibilities:
1.  one intersection point (this is the 'usual' case)
2.  one entire line (this is the case here)
3.  NO solution because there are two parallel lines.
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04/12/17

Lauren J.

For my equations after I followed the steps provided I got 
x-6y=3
-x+6y=-3
 
So for my solution would I just put x-6y=3 as my solution?
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04/12/17

Kenneth S.

Yes, that's the equation of the line. They're equivalent (their sum gives 0 = 0), proof of 'dependence.'
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04/12/17

Lauren J.

So would my answer be (0,0)? Like what does dependent mean?
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04/12/17

Kenneth S.

NO...ALL OF US TUTORS HAVE SAID THAT THIS SOLUTION IS ONE LINE.
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04/12/17

Mark M.

The solution is the set of all real numbers, ℜ
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04/12/17

Lauren J.

...sorry that I didn't understand. I was just asking a question and trying to get clearification. I didnt think that I was being rude or anything. No need to send me something in all caps and treat me with little to no respect. I appreciated your advice, and I thought you were a great help to me, but again i don't believe that you should talk to someone like that. And btw when I did put the equation of the line in as my answer on my homework it said that it was incorrect, that is why I was just asking if I was wrong. 
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04/12/17

Kenneth S.

1.  I was not being rude. I was emphasizing the answer (reiterating it).
2. You have said that when I did put the equation of the line in as my answer on my homework it said that it was incorrect. Your answer reveals that you were dealing with some sort of online software. Possibly they required the form of the equation to be y = mx+b, or in standard form Ax+By=C.  You have the right to appeal to your human teacher and show that your answer is correct, AND YOU SHOULD NOT BE PENALIZED FOR SOFTWARE SHORTCOMINGS (lack of clear instructions as to the format of your answer).
3.  I see that one tutor has supplied this Comment: The solution is the set of all real numbers, ℜ
I believe that this is misleading, because the solution is a set of ordered pairs; x can be anything, but the y's are DEPENDENT (obtained by solving for y, with any given x as input).
4. You need to review the ideas of functions and independent variable (inputs from the domain) and dependent variable (outputs, constituting the range).
5. We tutors who answer questions through the WyzAnt Answers Resource do so for free. We believe that our services have value, and we appreciate acknowledgment from those who benefit from our insight and time devoted to students. 
6. Do not confuse pointed guidance, especially when it is necessary to correct any misunderstanding of an answer, with rudeness. Rudeness stems not from choice of upper or lower case, but from wording. 
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04/13/17

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