Question

The roof lines of a building can be described by the system of equations below, where the floor is represented by the x-axis and the y-axis and the height of the building is along the z-axis. Measurements are in feet. Find the point of intersection of the roof lines, using an ordered triple in the form (x, y, z).

{ x+y+z=52,
3x-2y+z=69,
-x+2y-z=-59}


also part 2:
a support column will be placed under the intersection point. the column must be _____ feet to reach from the floor to the intersection point.
someone help me please?

Answer 1

add equations 1 and 3
x+y+z=53 -x+2y-z=-59 3y = -6 y = -2
substitute y=-2 into the first and second
x + z = 55 3x + z = 65 subtract first above from second above 2x = 10 x=5 substitute these two values into first (or any for that matter) equation to get z = 50
(5,-2,50)
the height of the column is 50 feet