Solving Systems Of Three Equations with Elimination

-x-5y-5z=2 4x-5y+4z=19 x+5y-z=-20

x=-2 y=-3 z=3

−5x + 3y + 6z = 4 −3x + y + 5z = −5 −4x + 2y + z = 13

x=-2 y=4 z=-3

−4x − 5y − z = 18 −2x − 5y − 2z = 12 −2x + 5y + 2z = 4

x=-4 y=0 z=-2

x − y − 2z = −6 3x + 2y = −25 −4x + y − z = 12

x=-5 y=-5 z=3

x − 6y + 4z = −12 x + y − 4z = 12 2x + 2y + 5z = −15

x=0 y=0 z=-3

−3a − b − 3c = −8 −5a + 3b + 6c = −4 −6a − 4b + c = −20

x=2 y=2 z=0

−6x − 2y − z = −17 5x + y − 6z = 19 −4x − 6y − 6z = −20

x=2 y=3 z=-1

4x + 4y + z = 24 2x − 4y + z = 0 5x − 4y − 5z = 12

x=4 y=2 z=0

−6r + 5s + 2t = −11 −2r + s + 4t = −9 4r − 5s + 5t = −4

x=4 y=3 z=-1

5x − 4y + 2z = 21 −x − 5y + 6z = −24 −x − 4y + 5z = −21

x=5 y=-1 z=-4

Write a system of equations with the solution (2, 1, 0).

Many answers. Ex: x + y + z = 3 2x + y + z = 5 x + 2y − z = 4

3a − 3b + 4c = −23 a + 2b − 3c = 25 4a − b + c = 25

no solution

5a + 5b + 5c = −20 4a + 3b + 3c = −6 −4a + 3b + 3c = 9

no solution

−6x − 2y + 2z = −8 3x − 2y − 4z = 8 6x − 2y − 6z = −18

no solution

4r − 4s + 4t = −4 4r + s − 2t = 5 −3r − 3s − 4t = −16

x=-1 y=-4 z=-4

−x − 5y + z = 17 −5x − 5y + 5z = 5 2x + 5y − 3z = −10

x=-1 y=-4 z=-4

6r − s + 3t = −9 5r + 5s − 5t = 20 3r − s + 4t = −5

x=-1 y=6 z=1