Answer
$k=2$ or $3$
Work Step by Step
Step 1. Add up the first and second equations to get $(k+1)x=12$ which gives $x=\frac{12}{k+1}$ (assume $k\ne -1$)
Step 2. Add up the second and third equations to get $(k-1)x=2k$ which gives $x=\frac{2k}{k-1}$ (assume $k\ne 1$)
Step 3. For the three lines to intersect at a single point, let $\frac{12}{k+1}=\frac{2k}{k-1}$ which gives $k^2+k=6k-6$ or $k^2-5k+6=0$
Step 4. Factor the above equation to get $(k-2)(k-3)=0$ which gives $k=2,3$
Step 5. When $k=2$ or $3$, the three lines intersect at a single point.
