Question

Find the value of m for which the system of equation 3x+y=1 and (2m-1)+x(m-1)y=2m+1 is inconsistent​

Answer 1

This system of equation is of the form

a1x+b1y+c1=0

a2x+b2y+c2=0

where a1=2m−1,b1=3,c1=−5 

and a2=3,b2=n−1 and c2=−2

For infinitely many solutions, we must have

a2a1=b2b1=c2c1

The given system of equations will have infinite number of solutions, if

32m−1=n−13=−2−5

⇒32m−1=

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