Answer
Infinitely many solutions.
Solution set:$\{(x,y,z)|2x-4y-z=2\}$
Work Step by Step
$-6x+12y+3z=-6$ Equation $(1)$
$2x-4y-z=2$ Equation $(2)$
$-x+2y+\frac{z}{2} =-1$ Equation $(3)$
$-\frac{1}{3} \times$ Equation $(1)$
$-\frac{1}{3}(-6x+12y+3z) = -\frac{1}{3}\times-6$
$2x-4y-z=2$ This is equivalent to Equation$(2)$
$-2 \times$ Equation $(3)$
$-2(-x+2y+\frac{z}{2}) = -2\times-1$
$2x-4y-z=2$ This is equivalent to Equation$(2)$
Since all three equations are identical and equivalent, they are dependent equations. Therefore, the system has infinitely many solutions.
Solution set:$\{(x,y,z)|2x-4y-z=2\}$
