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**spoc21** Find the equation of the plane that passes through the line of intersection of the planes x - 3y - 2z - 1 = 0 and 2x + 4y + z - 5 = 0 and parallel to the x-axis.

Find the line of intersection for the two planes:

1: 0t 3�� − 2�� − 1 = 0

2: 2�� + 4�� + �� − 5 = 0

let ��=�� (a scalar)

0��+3�� − 2�� − 1 = 0…(1)

2�� + 4�� + �� − 5 = 0.….(2)

use substitution to find the value of y from equation (1):

0��+3�� − 2�� − 1 = 0…………..(1)

3��= 2��+ 1

��=2��+13………(3)

eliminate the variable y from the equations:

First Multiply equation (1) by 4, and multiply equation (2) by -3:

0��+12�� −8�� − 4 = 0

−6��−12��−3��+15 = 0

Use the elimination method:

0��+12�� −8�� − 4 = 0

−6��−12��−3��+15 = 0

−6��−11��+11=0

−6��−11��=−11…(4)

−11��=−11+6��

��=−6��/11+1

y:

Substitute the value of z into equation (3):

��=2��+13

��=2(−6��/11+1)

��=(−4��−11)/11

I am very confused by the decimal values...Does my working make sense? I would appreciate any help