Question 377170
With 3 variables and 2 equations, you can eliminate any of the 3 variables and get the equation of a line.
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An equation in 3 variables is a plane in 3-space.  The 2 eqns are of 2 planes, and their intersection, which is a line in 3-space.  
By eliminating the x, you get the projection of the line onto the y-z plane.
By eliminating the y, you get the projection of the line onto the x-z plane.
By eliminating the z, you get the projection of the line onto the x-y plane.