Question

the pair of linear kx+2y=5 and 3x+y=1

Answer 1

The two equations kx+2y=5and 3x+y=1 represents two straight lines. For the equations to possess no solution, they must be parallel and not coincident.

For this we must have:

∣∣∣k321∣∣∣=0

⟹k−6=0

⟹k=6

Look at the graph. It will be clearer.

Here the blue line represents 3x+y=1 and the red line 6x+2y=5.