Find out The values for $a, b$ and $c$ [closed]

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$6a+4b+9c = -1$, $4a+6b+9c= -1$ and $9a+9b+17c= 1$



I want to know about that how we'll find out the values of $a, b$ and $c$ from the above equations. The answers are $a=-3.25, b= -3.5$ and $c= 3.5$.



But I'm not understanding how the answers have been calculated. Will someone help me out with the complete solution?




linear-algebra linear-transformations systems-of-equations




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closed as off-topic by Carl Mummert, Jendrik Stelzner, Claude Leibovici, TheSimpliFire, Clayton Aug 9 at 16:12


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Carl Mummert, Jendrik Stelzner, Claude Leibovici, TheSimpliFire, Clayton
If this question can be reworded to fit the rules in the help center, please edit the question.












  • perhaps you might want to include what do you don't understand about the solution? or you might be given another solution that you do not understand again
    – Siong Thye Goh
    Aug 6 at 6:41










  • I just want to see the calculations of finding out the values for a,b and c
    – Rizwan ashraf
    Aug 6 at 6:42










  • Have you tried Cramer's rule ?? @Rizwanashraf
    – Anik Bhowmick
    Aug 6 at 6:43










  • Thank's Anik for your help
    – Rizwan ashraf
    Aug 6 at 7:17














up vote
-2
down vote

favorite












$6a+4b+9c = -1$, $4a+6b+9c= -1$ and $9a+9b+17c= 1$



I want to know about that how we'll find out the values of $a, b$ and $c$ from the above equations. The answers are $a=-3.25, b= -3.5$ and $c= 3.5$.



But I'm not understanding how the answers have been calculated. Will someone help me out with the complete solution?




linear-algebra linear-transformations systems-of-equations




share|cite|improve this question













closed as off-topic by Carl Mummert, Jendrik Stelzner, Claude Leibovici, TheSimpliFire, Clayton Aug 9 at 16:12


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Carl Mummert, Jendrik Stelzner, Claude Leibovici, TheSimpliFire, Clayton
If this question can be reworded to fit the rules in the help center, please edit the question.












  • perhaps you might want to include what do you don't understand about the solution? or you might be given another solution that you do not understand again
    – Siong Thye Goh
    Aug 6 at 6:41










  • I just want to see the calculations of finding out the values for a,b and c
    – Rizwan ashraf
    Aug 6 at 6:42










  • Have you tried Cramer's rule ?? @Rizwanashraf
    – Anik Bhowmick
    Aug 6 at 6:43










  • Thank's Anik for your help
    – Rizwan ashraf
    Aug 6 at 7:17












up vote
-2
down vote

favorite









up vote
-2
down vote

favorite











$6a+4b+9c = -1$, $4a+6b+9c= -1$ and $9a+9b+17c= 1$



I want to know about that how we'll find out the values of $a, b$ and $c$ from the above equations. The answers are $a=-3.25, b= -3.5$ and $c= 3.5$.



But I'm not understanding how the answers have been calculated. Will someone help me out with the complete solution?




linear-algebra linear-transformations systems-of-equations




share|cite|improve this question













$6a+4b+9c = -1$, $4a+6b+9c= -1$ and $9a+9b+17c= 1$



I want to know about that how we'll find out the values of $a, b$ and $c$ from the above equations. The answers are $a=-3.25, b= -3.5$ and $c= 3.5$.



But I'm not understanding how the answers have been calculated. Will someone help me out with the complete solution?





linear-algebra linear-transformations systems-of-equations





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 6 at 12:10









Harry Peter

5,47311438




5,47311438









asked Aug 6 at 6:38









Rizwan ashraf

11




11




closed as off-topic by Carl Mummert, Jendrik Stelzner, Claude Leibovici, TheSimpliFire, Clayton Aug 9 at 16:12


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Carl Mummert, Jendrik Stelzner, Claude Leibovici, TheSimpliFire, Clayton
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Carl Mummert, Jendrik Stelzner, Claude Leibovici, TheSimpliFire, Clayton Aug 9 at 16:12


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Carl Mummert, Jendrik Stelzner, Claude Leibovici, TheSimpliFire, Clayton
If this question can be reworded to fit the rules in the help center, please edit the question.











  • perhaps you might want to include what do you don't understand about the solution? or you might be given another solution that you do not understand again
    – Siong Thye Goh
    Aug 6 at 6:41










  • I just want to see the calculations of finding out the values for a,b and c
    – Rizwan ashraf
    Aug 6 at 6:42










  • Have you tried Cramer's rule ?? @Rizwanashraf
    – Anik Bhowmick
    Aug 6 at 6:43










  • Thank's Anik for your help
    – Rizwan ashraf
    Aug 6 at 7:17
















  • perhaps you might want to include what do you don't understand about the solution? or you might be given another solution that you do not understand again
    – Siong Thye Goh
    Aug 6 at 6:41










  • I just want to see the calculations of finding out the values for a,b and c
    – Rizwan ashraf
    Aug 6 at 6:42










  • Have you tried Cramer's rule ?? @Rizwanashraf
    – Anik Bhowmick
    Aug 6 at 6:43










  • Thank's Anik for your help
    – Rizwan ashraf
    Aug 6 at 7:17















perhaps you might want to include what do you don't understand about the solution? or you might be given another solution that you do not understand again
– Siong Thye Goh
Aug 6 at 6:41




perhaps you might want to include what do you don't understand about the solution? or you might be given another solution that you do not understand again
– Siong Thye Goh
Aug 6 at 6:41












I just want to see the calculations of finding out the values for a,b and c
– Rizwan ashraf
Aug 6 at 6:42




I just want to see the calculations of finding out the values for a,b and c
– Rizwan ashraf
Aug 6 at 6:42












Have you tried Cramer's rule ?? @Rizwanashraf
– Anik Bhowmick
Aug 6 at 6:43




Have you tried Cramer's rule ?? @Rizwanashraf
– Anik Bhowmick
Aug 6 at 6:43












Thank's Anik for your help
– Rizwan ashraf
Aug 6 at 7:17




Thank's Anik for your help
– Rizwan ashraf
Aug 6 at 7:17










1 Answer
1






active

oldest

votes

















up vote
1
down vote













From the first and the second equations we'll get $a=b$, which gives
$$10a+9c=-1$$ and $$18a+17c=1.$$
Can you end it now?



I think the Cramer's rule it's very ugly here.



After summing of last two equations we obtain:
$$28a+26c=0$$ or
$$a=-frac13c14.$$
Thus,
$$10left(-frac13c14right)+9c=-1$$ or
$$left(-frac657+9right)c=-1$$ or
$$-frac27c=-1$$ or
$$c=3.5$$ and from here
$$a=-frac1314cdot3.5=-3.25,$$ which gives the answer:
$$(a,b,c)=(-3.25,-3.25,3.5).$$






share|cite|improve this answer























  • How we get a=b?
    – Rizwan ashraf
    Aug 6 at 6:44










  • Because $(6a+4b+9c)-(4a+6b+9c)=0.$
    – Michael Rozenberg
    Aug 6 at 6:45










  • If I follow this procedure I am getting the answer a=1 or I am doing something wrong.
    – Rizwan ashraf
    Aug 6 at 6:52










  • Yes, of course!
    – Michael Rozenberg
    Aug 6 at 6:53










  • But the actual answer of a is -3.25
    – Rizwan ashraf
    Aug 6 at 6:54

















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote













From the first and the second equations we'll get $a=b$, which gives
$$10a+9c=-1$$ and $$18a+17c=1.$$
Can you end it now?



I think the Cramer's rule it's very ugly here.



After summing of last two equations we obtain:
$$28a+26c=0$$ or
$$a=-frac13c14.$$
Thus,
$$10left(-frac13c14right)+9c=-1$$ or
$$left(-frac657+9right)c=-1$$ or
$$-frac27c=-1$$ or
$$c=3.5$$ and from here
$$a=-frac1314cdot3.5=-3.25,$$ which gives the answer:
$$(a,b,c)=(-3.25,-3.25,3.5).$$






share|cite|improve this answer























  • How we get a=b?
    – Rizwan ashraf
    Aug 6 at 6:44










  • Because $(6a+4b+9c)-(4a+6b+9c)=0.$
    – Michael Rozenberg
    Aug 6 at 6:45










  • If I follow this procedure I am getting the answer a=1 or I am doing something wrong.
    – Rizwan ashraf
    Aug 6 at 6:52










  • Yes, of course!
    – Michael Rozenberg
    Aug 6 at 6:53










  • But the actual answer of a is -3.25
    – Rizwan ashraf
    Aug 6 at 6:54














up vote
1
down vote













From the first and the second equations we'll get $a=b$, which gives
$$10a+9c=-1$$ and $$18a+17c=1.$$
Can you end it now?



I think the Cramer's rule it's very ugly here.



After summing of last two equations we obtain:
$$28a+26c=0$$ or
$$a=-frac13c14.$$
Thus,
$$10left(-frac13c14right)+9c=-1$$ or
$$left(-frac657+9right)c=-1$$ or
$$-frac27c=-1$$ or
$$c=3.5$$ and from here
$$a=-frac1314cdot3.5=-3.25,$$ which gives the answer:
$$(a,b,c)=(-3.25,-3.25,3.5).$$






share|cite|improve this answer























  • How we get a=b?
    – Rizwan ashraf
    Aug 6 at 6:44










  • Because $(6a+4b+9c)-(4a+6b+9c)=0.$
    – Michael Rozenberg
    Aug 6 at 6:45










  • If I follow this procedure I am getting the answer a=1 or I am doing something wrong.
    – Rizwan ashraf
    Aug 6 at 6:52










  • Yes, of course!
    – Michael Rozenberg
    Aug 6 at 6:53










  • But the actual answer of a is -3.25
    – Rizwan ashraf
    Aug 6 at 6:54












up vote
1
down vote










up vote
1
down vote









From the first and the second equations we'll get $a=b$, which gives
$$10a+9c=-1$$ and $$18a+17c=1.$$
Can you end it now?



I think the Cramer's rule it's very ugly here.



After summing of last two equations we obtain:
$$28a+26c=0$$ or
$$a=-frac13c14.$$
Thus,
$$10left(-frac13c14right)+9c=-1$$ or
$$left(-frac657+9right)c=-1$$ or
$$-frac27c=-1$$ or
$$c=3.5$$ and from here
$$a=-frac1314cdot3.5=-3.25,$$ which gives the answer:
$$(a,b,c)=(-3.25,-3.25,3.5).$$






share|cite|improve this answer















From the first and the second equations we'll get $a=b$, which gives
$$10a+9c=-1$$ and $$18a+17c=1.$$
Can you end it now?



I think the Cramer's rule it's very ugly here.



After summing of last two equations we obtain:
$$28a+26c=0$$ or
$$a=-frac13c14.$$
Thus,
$$10left(-frac13c14right)+9c=-1$$ or
$$left(-frac657+9right)c=-1$$ or
$$-frac27c=-1$$ or
$$c=3.5$$ and from here
$$a=-frac1314cdot3.5=-3.25,$$ which gives the answer:
$$(a,b,c)=(-3.25,-3.25,3.5).$$







share|cite|improve this answer















share|cite|improve this answer



share|cite|improve this answer








edited Aug 6 at 7:25


























answered Aug 6 at 6:42









Michael Rozenberg

88.2k1579180




88.2k1579180











  • How we get a=b?
    – Rizwan ashraf
    Aug 6 at 6:44










  • Because $(6a+4b+9c)-(4a+6b+9c)=0.$
    – Michael Rozenberg
    Aug 6 at 6:45










  • If I follow this procedure I am getting the answer a=1 or I am doing something wrong.
    – Rizwan ashraf
    Aug 6 at 6:52










  • Yes, of course!
    – Michael Rozenberg
    Aug 6 at 6:53










  • But the actual answer of a is -3.25
    – Rizwan ashraf
    Aug 6 at 6:54
















  • How we get a=b?
    – Rizwan ashraf
    Aug 6 at 6:44










  • Because $(6a+4b+9c)-(4a+6b+9c)=0.$
    – Michael Rozenberg
    Aug 6 at 6:45










  • If I follow this procedure I am getting the answer a=1 or I am doing something wrong.
    – Rizwan ashraf
    Aug 6 at 6:52










  • Yes, of course!
    – Michael Rozenberg
    Aug 6 at 6:53










  • But the actual answer of a is -3.25
    – Rizwan ashraf
    Aug 6 at 6:54















How we get a=b?
– Rizwan ashraf
Aug 6 at 6:44




How we get a=b?
– Rizwan ashraf
Aug 6 at 6:44












Because $(6a+4b+9c)-(4a+6b+9c)=0.$
– Michael Rozenberg
Aug 6 at 6:45




Because $(6a+4b+9c)-(4a+6b+9c)=0.$
– Michael Rozenberg
Aug 6 at 6:45












If I follow this procedure I am getting the answer a=1 or I am doing something wrong.
– Rizwan ashraf
Aug 6 at 6:52




If I follow this procedure I am getting the answer a=1 or I am doing something wrong.
– Rizwan ashraf
Aug 6 at 6:52












Yes, of course!
– Michael Rozenberg
Aug 6 at 6:53




Yes, of course!
– Michael Rozenberg
Aug 6 at 6:53












But the actual answer of a is -3.25
– Rizwan ashraf
Aug 6 at 6:54




But the actual answer of a is -3.25
– Rizwan ashraf
Aug 6 at 6:54


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