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## Solve the system of equations

x-4y-3z=21
2x-5y+12z=9
x-3y+3z=10

Hi Paula;
FIRST...x-4y-3z=21
SECOND...2x-5y+12z=9
THIRD...x-3y+3z=10
Let's note the fact that FIRST and THIRD include x with 1 as a coefficient.  Let's subtract the THIRD from the FIRST...
FIRST.......x-4y-3z=21
THIRD...-(x-3y+3z=10)
.............-y+6z=11
Isolate y...
...........-y=-6z+11
...........y=6z-11

Let's re-write the three equations, plugging this information in, thereby eliminating a variable...
FIRST...x-4y-3z=21
...........x-[4(6z-11)]-3z=21
...........x-24z+44-3z=21
............x-27z+44=21
...........x-27z=-23

SECOND...2x-5y+12z=9
...............2x-[5(6z-11)]+12z=9
...............2x-30z+55+12z=9
...............2x-18z+55=9
...............2x-18z=-46
Divide both sides by 2...
................x-9z=-23

THIRD...x-3y+3z=10
............x-[3(6z-11)]+3z=10
............x-18z+33+3z=10
............x-15z+33=10
............x-15z=-23

FIRST...x-27z=-23
SECOND...x-9z=-23
THIRD...x-15z=-23
z=0
x=-23

Original equations...
FIRST...x-4y-3z=21
..........-23-4y=21
..........-4y=44
............y=-11

SECOND...2x-5y+12z=9
.............................[(2)(-23)]-[(5)(-11)]=9
..............................-46+55=9
..............................9=9

THIRD.....x-3y+3z=10
.............-23-[(3)(-11)]=10
..............-23+33=10
...............10=10