Question

What is the line of intersection between the planes `3x+y-4z=2` and `x+y=18`?

Answer 1

`y+2z-26=0`

Explanation:

Equation of the line of intersection between the planes `3x+y-4z=2` and `x+y=18` can be obtained by putting the value of `x` from second equation into first.

As `x+y=18`, `x=18-y` and putting this in `3x+y-4z=2`, we get

`3(18-y)+y-4z=2` or

`54-3y+y-4z=2` or

`-2y-4z+52=0` or dividing each term by `-2`, we get

`y+2z-26=0`