Solution of equations

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mathdaemon

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Dec 26, 2012
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Hello

2a+0b+7c=0
3a+3b+6c=0

implies
a/-21=b/9=c/6

Please tell me how.

Thanks in advance
 
mathdaemon said:
2a+0b+7c=0
3a+3b+6c=0

implies
a/-21=b/9=c/6

Please tell me how.
Click to expand...
What have you tried so far? You solved the first equation for "a" in terms of "c", plugged this into the second equation, and... then what?

Please be complete, so we can see where you're getting stuck. Thank you! ;)
 
I recollect that this is related to proportions but I have no clue as to how it is being done.
Please help.
 
The problem, as stated, has nothing to do with "proportions" (except that the answer is stated as if it were a "proportion"). It is just a matter of combining equations to eliminate one variable.

For example, since you have
2a+0b+7c=0
3a+3b+6c=0

0b= 0 so 2a+ 7c= 0, 2a= -7c. Dividing both sides by both 2 and -7, because the answer you want has all numbers in the denominator, a/-7= c/2.

Of course, 2a= -7c is the same as a= -7c/2 and replacing a by that in the second equation,
3(-7c/2)+ 3b+ 6c= -21c/2+ 3b+ 12c/2= -9c/2+ 3b= 0 so 3b= -9c/2. Again, we want the numbers in the denominator so divide both sides by -9: b/-3= c/2.

Compare that to the previous result.
 
@HallsofIvy : Thank you vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv much.

@Denis : I am preparing for an exam to resurrect my life and career. I came across this while solving a problem on linear dependencies. Partly due to the ignorance and partly because of the kind of teachers during my engineering curricula, I have forgotten many such simple things. I will be posting now and then to clarify my silly doubts. :)

Thank you everyone
 
mathdaemon said:
@HallsofIvy : Thank you vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv much.

@Denis : I am preparing for an exam to resurrect my life and career. I came across this while solving a problem on linear dependencies. Partly due to the ignorance and partly because of the kind of teachers during my engineering curricula, I have forgotten many such simple things. I will be posting now and then to clarify my silly doubts. :)

Thank you everyone
Click to expand...

These types of problems are tackled during pre-calculus - either in high-school or first year college. These are pre-req for engineering curricula - not taught during engineering classes.
 
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