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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?

Verified Answer :

syed514

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

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