x-2y-3z=7 (a)

2x+y+z=-5 (b)

x+3y-2z=0 (c)

Eliminate x in (c)

x=-3y+2z (d)

Substitute into (d) to (a)

-5y-z=7

Multiply (a) by 2:

2x-4y-6z=14 (f)

Substract each side of (b) and (f):

5y+7z=-19 (g)

Eliminate y. add each side of (d) and (g) and solve for z:

6z=-12

z=-2

Solve for y using (g):

5y+7(-2)=-19

5y=-5

y=-1

Solve x using (c):

x+3(-1)-2(-2)=0

x-3+4=0

x+1=0

x=-1

2x+y+z=-5 (b)

x+3y-2z=0 (c)

Eliminate x in (c)

x=-3y+2z (d)

Substitute into (d) to (a)

-5y-z=7

Multiply (a) by 2:

2x-4y-6z=14 (f)

Substract each side of (b) and (f):

5y+7z=-19 (g)

Eliminate y. add each side of (d) and (g) and solve for z:

6z=-12

z=-2

Solve for y using (g):

5y+7(-2)=-19

5y=-5

y=-1

Solve x using (c):

x+3(-1)-2(-2)=0

x-3+4=0

x+1=0

x=-1