Use the​ Gauss-Jordan method to solve the system of equations. y=-9+x y=-5+z z=6-x

Answer 1

Please note that there are many ways to do this problem. This just happens to be one way. It may or may not match with the steps someone else uses.

Explanation:

1) Convert the equations into a matrix (position 1). Multiply Row 1 by "-1", add to Row 3 and replace Row 3 with the results to get position 2

2) Multiply Row 2 by "-1", add to Row 3 and replace Row 3 with the results to get position 3.

3) Divide Row 3 by 2 to get Position 4

4) Add Rows 3 and 2 and replace Row 2 with the result to get position 5

5) Add Rows 2 and 2 and replace Row 2 with the result to get position 6.

Interpret position 6 to get the answer: x = 5, y = -4, z = 1

Answer 2

the solution set is (x=5, y=-4, z=1)

rewriting:

-x + y + 0z = -9

0x + y - z = -5

z + 0y + z = 6

So then the matrix is:

-1 1 0 -9

0 1 -1 -5

1 0 1 6

adds row3 + row1 --> row1

0 1 1 -3

0 1 -1 -5

1 0 1 6

adds row2 + row1 --> row1

0 2 0 -8

0 1 -1 -5

1 0 1 6

so then 2y = -8

y = -4

equation 2 says: y - z = -5

-4 - z = -5

-z = -1

z = 1

original first equation says: -x + y = -9

-x + -4 = -9

-x = -5

x = 5

the solution set is (x=5, y=-4, z=1)