SOLUTION: Indicate if the following set of lines are parallel, perpendicular, neither. Show your work 3x+y=5 x+y=3 After finding the slope, and intercept, I think they are parallel.

Algebra ->  Linear-equations -> SOLUTION: Indicate if the following set of lines are parallel, perpendicular, neither. Show your work 3x+y=5 x+y=3 After finding the slope, and intercept, I think they are parallel.      Log On


   

Question 169128: Indicate if the following set of lines are parallel, perpendicular, neither.
Show your work
3x+y=5
x+y=3
After finding the slope, and intercept, I think they are parallel. just need verification.
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%2By=5 Start with the first equation.


y=5-3x Subtract 3x from both sides.


y=-3x%2B5 Rearrange the terms.


So we can see that the equation y=-3x%2B5 has a slope m=-3 and a y-intercept b=5.


x%2By=3 Now move onto the second equation.


y=3-x Subtract x from both sides.


y=-x%2B3 Rearrange the terms.


So we can see that the equation y=-x%2B3 has a slope m=-1 and a y-intercept b=3.


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So the slope of the first line is m=-3 and the slope of the second line is m=-1.


So the two slopes are NOT equal. This means that the two lines are NOT parallel.


Also, notice that if we multiply the slopes, we get %28-3%29%28-1%29=3 which is NOT equal to -1.
This means that the two slopes are NOT inverse reciprocals of one another.
So the two lines are NOT perpendicular



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Answer:


So the two lines are neither parallel nor perpendicular.