Correct Answer - Option 4 : x + 4y - 11 = 0
Concept:
The equation of the line with points (x1, y1) and (x2, y2)
\(\rm {y\ -\ y_1\over x \ -\ x_1} = {y_2\ -\ y_1\over x_2\ -\ x_1}\)
Calculation:
Given lines x - y + 4 = 0 ---(i)
y - 2x - 5 = 0 ---(ii)
Adding the 2 equation (i) and (ii)
-x - 1 = 0
x = -1
Putting it in equation (i)
-1 - y + 4 = 0
y = 3
Intersection of the lines (-1, 3)
Now the equation of the line to be find out is
\(\rm {y\ -\ 3\over x \ -\ (-1)} = {2\ -\ 3\over 3\ -\ (-1)}\)
4(y - 3) = -1(x + 1)
4y + x - 11 = 0