How do you find the X, Y, Z?

Question

2x + 2y + 3z = -1
3x - 1y - 2z = 18
-3x + 1y - 1z = -9

Answer 1

2x+2y+3z=-1 .....(1)
3x-1y-2z=18 .......(2)
-3x+1y-1z=-9 ......(3)

(1)+(2)x2
2x+2y+3z=-1
6x-2y-4z=36
-------------------+
8x-z=35 .............(4)

(2)+(3)
3x-1y-2z=18
-3x+1y-1z=-9
---------------------+
-3z=9
z=-3

substitute this value of z to (4)
8x-z=35
8x-(-3)=35
8x+3=35
8x=32
x=4

substitute the value of x and z to (1)
2x+2y+3z=-1
2(4)+2y+3(-3)=-1
8+2y-9=-1
2y-1=-1
2y=0
y=0

(x,y,z)=(4,0,-3)

hope this is clear enough

Answer 2

2x+2y+3z=-1..eqn1
3x-1y-2z=18....eqn2
-3x+1y-1z=-9...eqn3
add eqn2 and eqn3
-3z=18-9 = 9
so z=9/-3 =-3
substitute for z in eq1
2x+2y+3*-3=-1
2x+2y-9=-1
adding 9 to both sides
2x+2y =8...eqn 4
substitute for z in eq2
3x-1y-2*-3=18
3x-1y+6=18
subtracting 6 from both sides
3x-1y= 12...eqn5
mutiply both sides of eqn5 by 2
6x-2y=24..eqn6
add eqn4 and eqn6
8x=32
so x=4
sustitute for x in eqn4
2*4+2y=8
8+2y =8
subtracting 8 from both sides
2y=i.e y=0
x=4, y=0 and z=-3
(if you substitute these values of x., y and z in the left hand side of eqns 1, 2 and 3 you will get the numerical value of right hand side of those eqns)

Answer 3

add the second two equations:
-3z=9
z=-3
substitute this z value into the other two eqautions and use simultaneous eqautions to solve for x and y.

alternately you could do a gauss reduction. check you textbook or the web to find out how. its really easy but long to explain