Download Elimination

Elimination
3 variable
3 equation systems
Process for Elimination
1. Put all equations in order of ax+by+cz=d
1st  x  y  z  4

2nd  2 x  y  z  3
3rd  4 x  2 y  z  1
2. Use first equation to get rid of x terms in the
2nd and 3rd equations
First equation will stay the same, the second and
third will change no x values
Step 2
 2( x  y  z  4)
 2 x  2 y  2 z  8
2x  y  z  3
 3y  z   5
4( x  y  z  4)
4 x  4 y  4 z  16
 4 x  2 y  z  1
6 y  3 z  15
 x yz 4

  3 y  z  5

6 y  3 z  15

Cont’d
3. Use new second equation to get rid of y value in new
third equation
The second equation shouldn’t change, but you get
a new third equation
2(3 y  z  5)
 6 y  2 z  10
6 y  3 z  15
z 5
 x yz 4

  3 y  z  5

z 5

4. Solve new third equation for z
Cont’d
5. Back substitute to find y
 3 y  (5)  5
 3y  0
y0
5. Back substitute to find x x  (0)  (5)  4
x  1
5. Check ordered triple in original 2nd and 3rd
2(1)  (0)  5
equations
(1,0,5)
 2  5  3T
 4(1)  2(0)  (5)  1
4  0  5  1T
Try as groups
 x  y  2z  3

 x yz 0
3 x  2 y  z  1
