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## Homework Statement

Find the parametric equations of the intersection line of two planes 2x - 3y - z + 1 = 0 and

3x - 2y + 3z - 4 = 0

## Homework Equations

N/A

## The Attempt at a Solution

First I'll label them:

2x - 3y - z + 1 = 0 [1]

3x - 2y + 3z - 4 = 0 [2]

Then I get rid of the z variable for now, and multiply [1] by 3 to do that, then eliminate by adding:

6x - 9y - 3z +3 = 0

3x - 2y + 3z - 4 = 0

_________________

9x - 11y - 1 = 0 [3]

Then I write y in terms of x:

y = (9/11)x - 1/11[4]

Then substitute [4] back into [1]:

2x - 3((9/11)x - 1/11) - z +1 = 0

2x - (27/11)x +3/11 - z + 1 = 0

Then write z in terms of x:

z = (-5/11)x + 14/11

Finally, I set x = t to write the parametric equations:

x = t

y = (9/11)t - 1/11

z = (-5/11)t + 14/11

However, this was the answer my book got:

x = (11/9)t + 1/9

y = t

z = (-5/11)t + 11/9

Can anyone help me figure out what I did wrong? I double checked all the tedious calculations, and they seem correct to me. Thanks in advance.