We know that the system of equationsa1x+b1y=c1a2x+b2y=c2
has no solution, if
a1a2=b1b2≠c1c2
Here, a1=3,b1=1,c1=1,a2=2k−1,b2=k−1,c2=2k+1
So, the given system of equations will have no solution, if
32k−1=1k−1≠12k+1
32k−1=1k−1 and 1k−1≠12k+1
Now,
32k−1=1k−1⇒3k−3=2k−1⇒k=2
Clearly, for k=2 we have 1k−1≠12k+1
Hence, the given system of equations will have no solution, if k=2.