Answer
$\{\left(\frac{1}{2},\frac{1}{3},-1 \right ) \}$.
Work Step by Step
The given equations are
$\Rightarrow 3(2x+y)+5z=-1$
Apply distributive property
$\Rightarrow 6x+3y+5z=-1$ ......(1)
$\Rightarrow 2(x-3y+4z)=-9$
Apply distributive property
$\Rightarrow 2x-6y+8z=-9$......(2)
$\Rightarrow 4(1+x)=-3(z-3y)$
Apply distributive property
$\Rightarrow 4+4x=-3z+9y$
Add $+3z-9y-4$ to both sides.
$\Rightarrow 4+4x+3z-9y-4=-3z+9y+3z-9y-4$
Add like terms.
$\Rightarrow 4x-9y+3z=-4$......(3)
Multiply equation (1) by $2$.
$\Rightarrow 12x+6y+10z=-2$ ......(4)
Now add equations (2) and (4).
$\Rightarrow 2x-6y+8z+12x+6y+10z=-9-2$
Add like terms.
$\Rightarrow 14x+18z=-11$ ...... (5)
Multiply equation (1) by $3$.
$\Rightarrow 18x+9y+15z=-3$.......(6)
Now add equation (3) and (6).
$\Rightarrow 4x-9y+3z+18x+9y+15z=-4-3$
Add like terms.
$\Rightarrow 22x+18z=-7$......(7)
Subtract equation (5) from equation (7).
$\Rightarrow 22x+18z-(14x+18z)=-7-(-11)$
Simplify.
$\Rightarrow 22x+18z-14x-18z=-7+11$
$\Rightarrow 8x=4$
Divide both sides by $8$.
$\Rightarrow x=\frac{1}{2}$
Substitute the value of $x$ into equation (5).
$\Rightarrow 14(\frac{1}{2})+18z=-11$
Simplify.
$\Rightarrow 7+18z=-11$
Subtract $7$ from both sides.
$\Rightarrow 7+18z-7=-11-7$
Simplify.
$\Rightarrow 18z=-18$
Divide both sides by $18$.
$\Rightarrow z=-1$
Substitute the values of $x$ and $z$ into equation (1).
$\Rightarrow 6(\frac{1}{2})+3y+5(-1)=-1$
Simplify.
$\Rightarrow 3+3y-5=-1$
$\Rightarrow 3y-2=-1$
Add $2$ to both sides.
$\Rightarrow 3y-2+2=-1+2$
Simplify.
$\Rightarrow 3y=1$
Divide both sides by $3$.
$\Rightarrow y=\frac{1}{3}$
The solution set is $\{(x,y,z)\}=\{\left(\frac{1}{2},\frac{1}{3},-1 \right ) \}$.
