Question

Determine the values of a and b so that 2x - (a - 4)y = 2b + 1 and 4x - (a - 1)y = 5b -
1 have infinite number of solutions.

Answer 1

To have infinite number of solutions the ratio of corresponding coefficients should be same in both the equation , so that there is actually only one equation.

So
$\frac{2}{4} = \frac{a-4}{a-1} = \frac{2b-1}{5b-1}$

Solving the above relation we get 
a=7
b=-1