Originally Posted by

**HallsofIvy** I presume that by "region given" you mean the region **bounded** by those planes. Of course, x= 0, y= 0, and z= 0 are the coordinate planes so this region is in the first octant. x+ y= 4 is the plane crossing x= 0 in the line y= 4 and crossing the plane y= 0 in the line x= 0.

x= z- y- 1, equivalently, x+ y- z= -1, cuts the x= 0 plane in the line y- z= -1, the y= 0 plane in the line x- z= -1, and the z= 0 plane in the line x+ y= -1. The two planes, x+ y= 4, equivalent to x= 4- y, and x= z- y- 1 in the line x= 4- t, y= t, z= 5.