The original poster seeks to find the parametric equations for the line of intersection of two planes defined by the equations z=x+y and 2x-5y-z=1.
The discussion is ongoing, with participants providing feedback on each other's attempts and clarifying steps taken in their reasoning. Some guidance has been offered regarding the manipulation of the equations, but there is no explicit consensus on the correct approach or final expressions.
Participants note confusion regarding the methods used and the assumptions made during the problem-solving process. There is an emphasis on the need for clarity in the steps taken to arrive at the parametric equations.
Jaqsan said:Also, it would be helpful if you solved it with the elimination method because that's the way we were shown in class.
Yes, this is correct.Jaqsan said:First thing I did was eliminate x.
Rearranged the first equation to get, x+y-z=0 -------(3)
Multiplied (3) through by 2 to get, 2x+2y-2z=0 -------(4)
Subtracted (2) from (4) to get, 7y-z=-1 or y=(z-1)/7 ----(5)
Let z=t, so I got y=(t-1)/7.
This is incorrect. Multiplying x+y- z= 0 by 5 gives 5x+ 5y- 5z= 0. Adding that to 2x- 5y- z= 1 gives 7x- 6z= 1 so that 7x= 1+ 6z, x= (1+ 6z)/7, not "-7".Did the same thing for y, multiplying the first equation through by -5. And I got my final answer to be
x=(1+6t)/(-7) then z=t
You understand that there can be many different parameters for the same line don't you?The answers are x=6t, y=(-1/6)+t, z=(-1/6)+7t
My process could be completely wrong, which is why I need someone to help me out from the top. I'm just so confused.
HallsofIvy said:Adding that to 2x- 5y- z= 1 gives 7x- 6z= 1 so that 7x= 1+ 6z, x= (1+ 6z)/7, not "-7".
I added 5x+ 5y- 5z= 0 to 2x- 5y- z= 1 in order to eliminate "y"": 5y- 5y= 0.Jaqsan said:Okay, Why did you add the two equations?
What two parts are you talking about? I did add both parts of the equations: on the left (5x+ 5y- 5z)+ (2x-5y- z)= (5x+ 2x)+ (5y- 5y)+ (-5z- z)= 7x- 6z and on the right 0+ 1= 1instead of subtract like in the first one. Aren't you supposed to do the same thing to both parts?
Hmmmm...I didn't know that about the final answer. Must have missed it in class. Now let's just clarify the middle part. Thanks and thanks in advance! :-).