# System of equations problem?

What is x+y+z=6, x-y-z=-4, 2x+y-4z=-8 as an augmented matrix? How would you solve this using the Gauss-Jordan method?

### 2 Answers

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- hayharbrLv 76 months ago
1 1 1 6

1 -1 -1 -4

2 1 -4 -8

Add row 2 to row 1 making a new row 1,

then add row 3 to row 2 making a new row 2

2 0 0 2

3 0 -5 -12

2 1 -4 -8

Subtract r1 from r3 then divide r1 by 2

1 0 0 1

3 0 -5 -12

0 1 -4 -10

Multiply row 1 by -3 and add to r2

1 0 0 1

0 0 -5 -15

0 1 -4 -10

Divide r2 by -5

1 0 0 1

0 0 1 3

0 1 -4 -10

Multiply r2 by 4 and add to r3

1 0 0 1

0 0 1 3

0 1 0 2

so x = 1, y = 2 and z = 3

- sepiaLv 76 months ago
x + y + z = 6, x - y - z = -4, 2x + y - 4z = -8

2x = 2, x = 1, y + z = 5, 3x - 5z = -12, z = -3

x = 1, y = 8, z = -3

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