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Question 57
Let P be the point of intersection of the lines
3x + 4y = 2a and 7x + 2y = 2018
and Q the point of intersection of the lines
3x + 4y = 2018 and 5x + 3y = 1
If the line through P and Q has slope 2, the value of a is:
Solution
On solving for x and y from the equations
3x + 4y = 2018 and 5x + 3y = 1
we get Q(-550,917)
Let, P(x,y)
So, $$\frac{y - 917}{x + 550}$$ = 2
=> y - 2x = 2017 ....(1)
Considering the equations
3x + 4y = 2a ........(2)
7x + 2y = 2018 .....(3)
On subtracting equation (2) from (3) we have,
4x - 2y = 2018 - 2a
=> 2x - y = 1009 - a
=> y - 2x = a -1009 .....(4)
From equation (1) and (4)
2017 = a - 1009
=> a = 3026
Hence, option C.
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