Solve the following system of equations and give a geometrical interpretation of the result.

x + y + z = 6

2x + y − 3z = -5

4x − 5y + z = −3

Give a geometrical interpretation of the intersection of the planes with equations

x + y − 3 = 0

y + z + 5 = 0

x + z + 2 = 0

Determine a scalar equation for the plane that passes through the point (2, 0, −1) and is perpendicular to the line of intersection of the planes

2x + y – z + 5 = 0 and x + y + 2z + 7 = 0.