Answer
Infinitely many solutions.
Solution set: $\{ (x,y,z)|x-2y+z=-5\}$
Work Step by Step
$x-2y+z=-5$ Equation $(1)$
$-3x+6y-3z=15$ Equation $(2)$
$2x-4y+2z=-10$ Equation $(3)$
Divide both sides of Equation $(2)$ by $-3$ and Equation $(3)$ by $2$, the resulting system is
$x-2y+z=-5$
$x-2y+z=-5$
$x-2y+z=-5$
All three equations are identical and equivalent. The equations are dependent equations. So, the system has infinitely many solutions.
Solution set: $\{ (x,y,z)|x-2y+z=-5\}$