Find the equation of a straight line passing through the point of intersection of the line 5 x minus 6 squared minus 1 is equal to zero and 3 x + 2 y + 5 is equal to zero and perpendicular to the line 3 x minus 5 y + 11 is equal to zero
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Firstly , we should find out intersecting point of given lines 5x -3y = 1 and 2x + 3y = 23.
5x - 3y = 1 ------(1)
2x + 3y = 23 ------(2)
add equations (1) and (2) ,
7x = 24 ⇒ x = 24/7 , put it in equation (1)
3y = 120/7 -1 ⇒y = 113/21
Hence, unknown line is passing through the point (24/7 , 113/21)
now, unknown line is perpendicular upon 5x - 3y = 1
Means, slope of unknown line ×{ slope of 5x - 3y = 1} = -1
Let slope of unknown line is m
∴ m × 5/3 = -1 ⇒ m = -3/5
Now, equation of unknown line is ,
(y - 113/7) = -3/5(x - 24/7)
⇒5y - 565/7 + 3x - 72/7 = 0
⇒ 3x + 5y - 91= 0
Hence, answer is 3x + 5y = 91