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What is the equation of the straight line which joins the intersection of the line x - y + 4 = 0 and y - 2x - 5 = 0 and the point (3, 2)?
1. x + y - 11 = 0
2. x - 2y - 11 = 0
3. x + 3y - 11 = 0
4. x + 4y - 11 = 0

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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

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