Linear Equation in Two Variables

Question

Find the values of k for which the system of equation kx-y=2, 6x-2y=3 has 1. A unique solution 2. No solution

Answer 1

$$6x-2y=3$$ So $$y=3x-3/2$$ Sub into the first equation $$kx-3x+3/2=2$$ $$(k-3)x=1/2$$

So for all $k\ne 3$ it has a unique solution $$x=\frac{1}{2k-6}$$

And for $k=3$, it has no solution.