Question

2x-y+3z=9,x+y+z=6,x-y+z=2 by using gauss jordan method​

Answer 1

x + y + z = −2

2 x − 3 y + 4 z = 14

5 x + 2 y − 3 z = 10

[STATE 1] Express z in terms of x and y:

x + y + z = −2

2 x − 3 y + 4 (−2 − x − y) = 14

5 x + 2 y − 3 (−2 − x − y) = 10

[STATE 2] Simplify the equations:

x + y + z = −2

−2 x − 7 y = 22

8 x + 5 y = 4

[STATE 3] Express x in terms of y:

x + y + z = −2

−2 x − 7 y = 22

−4 (22 + 7 y) + 5 y = 4

[STATE 4] Simplify the equation:

x + y + z = −2

−2 x − 7 y = 22

y = −4

[STATE 5] Reach the solution:

x = 3

y = −4

z = −1