3 Variable System of Equations When All Set to Zero

Question

-5x+4y-2z=0

x-2y+z=0

6x-6y+3z=0,

solve for x,y, and z.

Answer 1

the last equation is is 2x - 2y + z = 0

Pairs first and last: eliminates y by subtraction:

2x - 2y + z = 0

x - 2y + z = 0

--------------------------

x = 0

The system now becomes:

4y - 2z = 0

-2y + z = 0

-6y +3z= 0

2y - z = 0 <-- divides by 2

z = 2y <--- solves for z

2y - z = 0 <--- divides by -3

Subsitutes z= 2y into 2y - z = 0

It is 0 = 0

That is because all three equatons are the same

There are infinitely many solutions

x=0 and z = 2y