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=53 3x-2y+z=69 -x+2y-z=-59

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=53  3x-2y+z=69  -x+2y-z=-59

miracrown · Answer

ok, so we need to solve for (x,y,z)
we could use substitution, or a matrix
do you have a preference ?

kainui · Answer

This one's pretty nice, you can add the first equation to the last equation and both the x and z terms cancel out.

anonymous · Answer

I figured it out !!!

jack1 · Answer

$\large x+y+z=53 ~~~~\rightarrow ENQ~1$ 
so:
$\large x = 53-y-z~~~~ \rightarrow ENQ~1a$  

$\large -x+2y-z=-59  ~~~~\rightarrow ENQ~3$

sub EQN 1a into EQN 3

$\large -x+2y-z=-59  $
$\large -(53-y-z)+2y-z=-59  $
$\large -53+y+z+2y-z=-59  $
$\large 3y=-59+53  $

$\Large y=\frac {-6}3 = -2  $

now you know y, just continue from here with substitution until you know x and z
the intersection point will be at the 3 dimensional point (x,y,z)