The system won't have a unique solution when what appears to be two lines is really only one line. The coefficients in an equation for a line only matter in ratio; if we multiply them all by the same non-zero scalar we'll still have the same line, of course with an infinite number of points on it, our infinite number of solutions.
2x - y = 8
6x - 3y = 4a
We need these to be the same equation, meaning they have to have all the same solutions. So we have to figure out the factor to multiply the first equation by to get the second.
That factor is obviously 3 because 3(2x)=6x and 3(-y)=-3y. So we need the constants in the same ratio,
