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  •  For what values of m and n the following system of linear equations has infinitely many solutions.  <img alt="3x + 4y = 12 (m + n) x + 2 (m-n ) y = 5m -1" src="https://entrancecorner.codecogs.com/gif.latex?3x%20&plus;%204y%20%3

 For what values of m and n the following system of linear equations has infinitely many solutions.

 3x + 4y = 12 (m + n) x + 2 (m-n ) y = 5m -1

 

 

Answers (1)

equation are 

3x + 4y = 12 \\\\ (m+n)x + 2 (m-n)y = ( 5m-1)

to have infinite solution both equations should be the same 

\frac{m+n}{3} = \frac{2 (m-n)}{4} = \frac{5m-1}{12}

multiplying each with 12 

4 m + 4n = 6 m - 6n = 5 m -1

Taking first two terms 

4 m + 4n = 6 m - 6n

10 n = 2 m \\\\ m = 5 n ---- (1)

 taking 1st and 3rd term 

4 m + 4n = 5 m -1\\\\ m = 4 n +1 ---- ( 2 ) \\\\ by (1) \: \:and \: \: (2) \\\\ 5 n = 4 n+ 1 \\\\ n = 1 \\\\ m = 5

Posted by

Safeer PP

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