Let P be the point of intersection of the lines 2x + 3y = 3a and 3x – 4y = 8 and Q be the point of intersection of the lines x + 2y = 5 and 3x – y = 4. If the line passing through P and Q has slope 2, then the value of a is pls answer I will mark u brainliest
dont spam
Answers
Given : P point of intersection of the lines 2x + 3y = 3a and 3x – 4y = 8 and Q point of intersection of the lines x + 2y = 5 and 3x – y = 4
the line passing through P and Q has slope 2
To Find : value of a
Solution:
2x + 3y = 3a ..Eq1
3x – 4y = 8 ..Eq2
4 * Eq1 + 3 * eq2
8x + 9x = 12a + 24
=> 17x = 12(a + 2)
=> x = 12(a + 2)/17
3* eq1 - 2 * Eq2
=> 17y = 9a - 16
=> y = (9a - 16)/17
P ( 12(a + 2)/17 , (9a - 16)/17)
x + 2y = 5
3x – y = 4
=> x = 13/7 , y = 11/7
Q = ( 13/7 , 11/7)
Slope of PQ = ( (9a - 16)/17 - 11/7) / ( 12(a + 2)/17 - 13/7) = 2
=> (63a - 112 - 187) = 2 ( 84a + 168 - 221 )
=> 63a - 299 = 168a - 442
=> 105a = 143
=> a = 143/105
learn More:
the slope of the line 2x+2y =2 is equal to - Brainly.in
https://brainly.in/question/14696390
find the slope of the line joining the points 0, sin theta cos and Cos ...
https://brainly.in/question/14903494