SOLUTION: describe the relationship between the 2 lines 5y+3x=10 and 3y-5x=6 I have looked through my notes and have tried video math lessons but not finding the right one

Algebra ->  Graphs -> SOLUTION: describe the relationship between the 2 lines 5y+3x=10 and 3y-5x=6 I have looked through my notes and have tried video math lessons but not finding the right one       Log On


   

Question 431736: describe the relationship between the 2 lines 5y+3x=10 and 3y-5x=6 I have looked through my notes and have tried video math lessons but not finding the right one
Found 3 solutions by Gersid, mananth, htmentor:
Answer by Gersid(33) About Me  (Show Source):
You can put this solution on YOUR website!
You might see a relationship if you were to write these equations in slope-intercept form:
5y%2B3x+=+10--->y+=+%28-3%2F5%29x%2B10
3y-5x+=+6---->y+=+%285%2F3%29x%2B6
Do you see that the slopes are negative reciprocals of each other?
Two lines whose slopes are negative reciprocals are perpendicular.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
5y+3x=10
5y= -3x+10
/5
y= -3x/5 +2..............1
3y-5x=6
3y=5x+6
/3
y=5x/3+2
You find that the slopes of these two lines are negative reciprocal of each other. m1*m2=-1
3 x + 5 y = 10 .............1
-5 x + 3 y = 6 .............2
Eliminate y
multiply (1)by -3
Multiply (2) by 5
-9x-15y=-30
-25x+15y=30
Add the two equations
-34x=0
/-34
x=0
plug value of x in (1)
3x+5y=10
5y=10
5 y = 10
5 y = 10
y = 2
They intersect at (0,2)
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cy=%28-3x%2F5%29%2B2%2Cy=%285x%2F3%29%2B2%29%29


Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The equations in point-slope form are:
y = (-3/5)x + 2
y = (5/3)x + 2
Since the slopes are negative reciprocals of each other, the lines are perpendicular. And they have the same y-intercept, y=2
The graphs are shown below:
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%28-3%2F5%29x%2B2%2C%285%2F3%29x%2B2%29