4x + 2y + z = 10       (1)
 x +  y - z =  5       (2)
x ≥ 0, y  ≥0, z ≥ 0


The idea of the solution is THIS: 


    The given system of two equations defines a straight line in the space (x,y,z), which is the intersection 
    of the two relevant planes in .

    I am going to express this straight line as a parametric line of one argument and then express the OBJECTIVE function 
    as the function of the same argument


     In this way I will have a linear objective function  defined on the segment in the number line, and its minimum will be 
     at one of two endpoints of the segment.