SOLUTION: Decide whether the pair of lines is parallel, perpendicular or neither. 5x+3y=4 3x-5y=3

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Question 189774: Decide whether the pair of lines is parallel, perpendicular or neither.
5x+3y=4
3x-5y=3
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Given Line Eqn system%285x%2B3y=4%28red%28EQN1%29%29%2C3x-5y=3%28red%28EQN2%29%29%29

In red%28EQN1%29,
Let Fy=0:
5x%2B3%280%29=4 ---> cross%285%29x%2Fcross%285%29=4%2F5
red%28x=4%2F5%29, x-Intercept (4/5,0)

Let Fx=0
5%280%29%2B3y=4 ---> cross%283%29y%2Fcross%283%29=3%2F4
red%28y=4%2F3%29, y-Intercept (0,4/3)


In red%28EQN2%29,
Let Fy=0:
3x-5%280%29=3
3x=3 ---> cross%283%29x%2Fcross%283%29=cross%283%291%2Fcross%283%291
red%28x=1%29, x-Intercept

Let Fx=0:
3%280%29-5y=3
-5y=3 --->cross%28-5%29y%2Fcross%28-5%29=3%2F-5
red%28y=-3%2F5%29,y-Intercept


As we see the graph,
---> red%28RED=EQN1%29 is perpendicular to green%28GREEN=EQN2%29



To check, we know the Slope of one line is negative reciprocal of the other,m2=-1%2Fm%5B1%5D. We'll see:

In red%28EQN1%29, 5x+3y=4 ---> 3y=-5x%2B4 --->cross%283%29y%2Fcross%283%29=%28-5x%2B4%29%2F3
y=highlight%28%28-5%2F3%29%29x%2B%284%2F3%29, m%5B1%5D=-5%2F3

In red%28EQN2%29, 3x-5y=3 ---> 5y=3x-3 --->cross%285%29y%2Fcross%285%29=%283x-3%29%2F5
y=highlight%28%283%2F5%29%29x-3%2F5, m%5B2%5D=3%2F5

Verifying, m%5B2%5D=-1%2Fm%5B1%5D
3%2F5=-1%2F%28-5%2F3%29=%28-1%29%28-3%2F5%29
3%2F5=3%2F5

*The two lines are perpendicular (Answer)




Thank you,
Jojo