A system with (infinite/unique) solution will reduce to identity.

Solve the following system of linear equations in three variables:

$x+y+z=5; 2x-y+z=9; x-2y+3z=16$

Solve the following system of linear equations in three variables.

$\frac{1}{x}-\frac{2}{y}+4=0; \frac{1}{y}-\frac{1}{z}+1=0; \frac{2}{z}+\frac{3}{x}=14$

Solve the following system of linear equations in three variables.

$x+20=\frac{3y}{2}+10=2z+5=110-(y+z)$

Discuss the nature of solutions of the following system of equations.

$x+2y-z=6; -3x-2y+5z=-12; x-2z=3$

Discuss the nature of solutions of the following system of equations.

$2y+z=3(-x+1); -x+3y-z=-4; 3x+2y+z=-\frac{1}{2}$

Discuss the nature of solutions of the following system of equations.

$\frac{y+z}{4}=\frac{z+x}{3}=\frac{x+y}{2}; x+y+z=27$