Q42 of 54 Page 77

Find the value of m which the pair of linear equations 2x + 3y – 7 = 0 and (m – 1) x + (m + 1) y = (3m – 1) has infinitely many solutions.

Since, the pair of linear equations has infinitely many solutions


2x + 3y – 7 = 0 ……(1)


(m – 1) x + (m + 1) y = 3m – 1


(m – 1) x + (m + 1) y – 3m + 1 = 0 ……(2)


From equation (1) and (2)


a1 = 2


b1 = 3


c1 = – 7


a2 = m – 1


b2 = m + 1


c2 = – 3m + 1



2 (m + 1) = 3 (m – 1)


2m + 2 = 3m – 3


3m – 2m = 2 + 3


m = 5


Therefore, value of m is 5.


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