Answer
$k=\frac{1}{5}$
Work Step by Step
Step 1. Subtract equation 2 from 2 times the first equation and get $(2k-1)x+(2-k)z=0$
Step 2. For the system of equations to have infinitely many solutions, the above equation and equation3 must coincide, which means that the coefficients are proportional that is $\frac{2k-1}{-1}=\frac{2-k}{3}$
Step 3. Solve the above equation for $k$ to get $k=\frac{1}{5}$
