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

Algebra ->  Linear-equations -> SOLUTION: Decide whether the pair of lines is parallel, perpendicular or neither. 3x+5y=3 5x+3y=4      Log On


   



Question 189764: Decide whether the pair of lines is parallel, perpendicular or neither.
3x+5y=3
5x+3y=4

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There are actually (4) possibilities when given 2 equations
---------------
(1) They could actually be the SAME line
3x+%2B+2y+=+8
6x+%2B+4y+=+16
These are the same line because one is an
exact multiple of the other
---------------
(2) They can be parallel lines
If the slope of DISABLED_event_one= the slope of the other
---------------
(3) Perpendicular lines
If the slope of DISABLED_event_one= the negative reciprocal
of the slope of the other
---------------
(4) Two different lines, neither parallel nor perpendicular
----------------
3x+%2B+5y+=+3
5x+%2B+3y+=+4
These need to be put in the slope-intercept form
which is: y+=+mx+%2B+b (m is the slope)
3x+%2B+5y+=+3
Subtract 3x from both sides
5y+=+-3x+%2B+3
Divide both sides by 5
y+=+-%283%2F5%29x+%2B+3
Notice that m+=+-3%2F5
----------------
5x+%2B+3y+=+4
Subtract 5x from both sides
3y+=+-5x+%2B+4
Divide both sides by 3
y+=+-%285%2F3%29x+%2B+4
Notice m+=+-5%2F3
If this slope was 5/3, it would be perpendicular
to the other line.
----------------
These two lines are neither the same line, parallel, or
perpendicular. I'll plot them: