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Question 798041: Hello. Please help me! Due tomorrow :(
Find the equation of the line which passes through the point of intersection of the lines 2*x+y=8 and 3*x+2*y=0 and is
(A) perpendicular to the x-axis
(B) perpendicular to the y-axis
I know the beginning of it: (2x+y-8)+k*(3x+2y) = 0
Please help me!! Thanks
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The problem here is finding the point of intersection: (a,b).
After that, the line perpendicular to the x-axis, is a vertical line, and the equation of the vertical line passing through (a,b) is  ( does not play a part).
Similarly, the line perpendicular to the y-axis, is a horizontal line, and the equation of the horizontal line passing through (a,b) is 
We are looking for a pair (x,y) that satisfies  and  .
We need to solve  .
You seemed to be trying to solve the system by combining the equations, which always works, but in this case, I would prefer to solve by substitution.
Since the coefficient of in is  , I would solve the system by substitution starting by solving for .
(It seems easiest that way).
-->
Substituting into
 --> --> -->
That is the solution to part (A),
Then, returning to the solved , and plugging in  , I get
 ---> -->
That is the solution to part (B),
IN PICTURES:
 system solved, now the perpendicular lines 
ANOTHER WAY TO SOLVE THE SYSTEM:
This may be what you were trying to do. Names for this procedure may vary. It may be called "by combinations", or "by elimination", or even fancier names).
The ways to show the work vary even more.
--> --> --> --> -->
You can substitute into one of the equations to find or you can make a different combination.
--> --> --> -->
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