1. 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:
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By: anil on 05 May 2019 02.34 am
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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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.