SOLUTION: can you please help me indicate if the line is parallel, perpendicular, or neither. (((3x+y=5 -x+3y=6)))

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: can you please help me indicate if the line is parallel, perpendicular, or neither. (((3x+y=5 -x+3y=6)))      Log On


   

Question 153309This question is from textbook Algebra structure and method book 1
: can you please help me indicate if the line is parallel, perpendicular, or neither. (((3x+y=5 -x+3y=6))) This question is from textbook Algebra structure and method book 1

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
can you please help me indicate if the line is parallel, perpendicular, or neither.
system+%283x%2By=5%2C+-x%2B3y=6%29

Solve them both for y and look at their respective coefficients of x.
These coefficients are the slopes of the lines. 

1. If the are the same, the lines are parallel.
2. If they are not parallel, then find the reciprocal of one of those
   coefficients of x, then change the sign.  If that is the same as the 
   other coefficient of x, then they are perpendicular.

If neither, then neither!

Solve the first for y:

3x%2By=5

Add -3x to both sides:

3x%2By-3x=5-3x

cross%283x%29%2By-cross%283x%29=5-3x

y=5-3x  

The coefficient of x is -3

Solve the second for y:

-x%2B3y=6

Add +x to both sides:

-x%2B3y%2Bx=6%2Bx

cross%28-x%29%2B3y-cross%28x%29=6%2Bx

3y=6%2Bx  

Now we must multiply both sides by 1%2F3

%281%2F3%293y=%281%2F3%296%2B%281%2F3%29x

                2
%281%2Fcross%283%29%29cross%283%29y=%281%2Fcross%283%29%29cross%286%29%2B1%2F3x

y+=+2%2B1%2F3x


The coefficient of x is 1%2F3

------

So the two coefficients are -3 and 1%2F3

They certainly are not the same, so they are not parallel.

So let's find the reciprocal of the 1%2F3 which is
3%2F1 which equals 3 and then change the sign to 
-3.

We notice that we get the other.  So therefore they are perpendicular.

Edwin