Solve the system of equations

Question

x-4y-3z=21

2x-5y+12z=9

x-3y+3z=10

Answer 1

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