- #1

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**3x+3y+3z=3**

**x+y+z=-1**

3 3 3 | 3

1 1 1 |-1

1 1 1 | 0

0 0 0 | 1

x = -y -z

y = 1

Substitute y into x, x = -1 -z

Let z = t, tER

Then x = -1 -t, y = 1

The corresponding vector equation of the line intersection is:

(x,y,z) = (-1, 1, 0) + t(-1, 0, 1)

**Does that look right? This is my first time dealing with these.**