Of course the system has a solution, namely the ordered triple (0, 0, 0)
Nothing to write. The system is already written, namely:
x=0, y=0, and z=0
These are the equations of the three coordinate axes in
John
The student's error is that 0 is a number, and therefore is a perfectly good answer. This systemWe can eliminate y by adding the first two equations just as they are: x + y + z = 0 x - y + z = 0 ------------- 2x +2z = 0 We can eliminate y and z by adding the last two equations: x - y + z = 0 x + y - z = 0 ------------- 2x = 0 So we have the system: Solve the second one for s, 2x = 0 x = 0 Substitute in 2x + 2z = 0 2(0) + 2z = 0 2z = 0 z = 0 Substitute in one of the original equations: x + y + z = 0 0 + y + 0 = 0 y = 0 Edwin