Math problem

Question

4x-2y+z=0

x+y=0

-12x+6y-3z=0

 

I've tried solving this and got 0=0, which means there are infinite solutions. If this is true, z is any real number. What are is x and y? I tried this and got x=-z/6 and y=z/6. Is this correct?

Answer 1

You're correct about "infinitely many solutions.

 

Using my trusty TI-83 Plus, I got y -½z = 0 & x = 0 when I did the Reduced Row Echelon operation (rref) on the augmented matrix, which had all 0's on the bottom row of the matrix.  So z is the arbitrary variable.