The discussion centers on solving the Diophantine equation 7x + 4y = 100. Two participants present different solutions: one proposes x = 100 - 4t and y = 200 - 7t, while the other suggests x = 4t and y = 25 - 7t. Both solutions are valid under specific conditions, but the second solution is confirmed as correct by multiple contributors. The confusion arises from the application of the Diophantine method, highlighting the importance of accurate substitution in verifying solutions.
PREREQUISITESMathematicians, students studying number theory, and anyone interested in solving linear Diophantine equations.
Your answer is obviously incorrect. Using your result, 7x+4y=1500-56t. Your answer is correct for -7x+y=100.Ling Min Hao said:The given question required me to solve 7x+4y =100 by using diophantine equation . I get an answer for x = 100 - 4t and y = 200 - 7t . But his given answer is x = 4t and y = 25-7t . I think both of mine and the answer given is correct but I can't figure out how he get another solution
I think you mean -7x+4y=100.mathman said:Your answer is correct for -7x+y=100.
You are right - my typo.mfb said:I think you mean -7x+4y=100.
Both answer is correct since both can be used to find the value of x and y , it's just I don't understand how he get the answer using dio phantine methodmathman said:Your answer is obviously incorrect. Using your result, 7x+4y=1500-56t. Your answer is correct for -7x+y=100.
His answer is correct.
I am not familiar with the Diophantine method. However, by substituting your answer into the original equation, it is obviously wrong. His answer is obviously correct. I can only guess you are misusing the Diophantine method.Ling Min Hao said:Both answer is correct since both can be used to find the value of x and y , it's just I don't understand how he get the answer using dio phantine method