For all value of a and b the line ( a + 2b) x + (a - b) y + (a + 5b) = 0 passes through the point

 

The correct answer is: (-2, 1)

In this question we are given line   and we have to find the coordinates through which lines will pass irrespective of any values of 
For the lines to pass through a fixed point it must not depend on  on that point.
Therefore,
Step1: Rewriting the given equation of line.

Step2:  Taking the terms related to  common
=>
Step3:  For the line to pass through a fix point the coefficient of  must be zero
Therefore.
 and 
Step4: Solving for the points
For finding the values of x and y we need to solve above two linear equation in two variable.

By adding both the equation we get

=>
Now we will substitute the value of x in any one of the above equation to find y.

So .
Hence, for any value of  the line must pass through .