Hi Paula;
FIRST...x4y3z=21
SECOND...2x5y+12z=9
THIRD...x3y+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.......x4y3z=21
THIRD...(x3y+3z=10)
.............y+6z=11
Isolate y...
...........y=6z+11
...........y=6z11
Let's rewrite the three equations, plugging this information in, thereby eliminating a variable...
FIRST...x4y3z=21
...........x[4(6z11)]3z=21
...........x24z+443z=21
............x27z+44=21
...........x27z=23
SECOND...2x5y+12z=9
...............2x[5(6z11)]+12z=9
...............2x30z+55+12z=9
...............2x18z+55=9
...............2x18z=46
Divide both sides by 2...
................x9z=23
THIRD...x3y+3z=10
............x[3(6z11)]+3z=10
............x18z+33+3z=10
............x15z+33=10
............x15z=23
FIRST...x27z=23
SECOND...x9z=23
THIRD...x15z=23
z=0
x=23
Original equations...
FIRST...x4y3z=21
..........234y=21
..........4y=44
............y=11
SECOND...2x5y+12z=9
.............................[(2)(23)][(5)(11)]=9
..............................46+55=9
..............................9=9
THIRD.....x3y+3z=10
.............23[(3)(11)]=10
..............23+33=10
...............10=10
Mar 10

Vivian L.