My textbook has this system of equations,
$$x-y+5z = 3 \\ 2x+3y-z = 2 \\ -4x-y-9z = -8$$
The answer it lists is $(0, 13/14, 11/14)$. I can get the answer by eliminating $y$ or $z$, but when I eliminate with $x$, I get an infinite solution.
I multiply the first equation by $-2$ and add it with the second equation to get $5y - 11z = -4$. Then I multiply the second equation by $-2$ and add it with the third equation to get $5y - 11z = -4$ too! I did the calculations many times and I'm still confused!! I used all three equations by eliminating $x$ yet still got infinite solution.