Question

X + 2y + z = 4

2x - y + 4z = - 8

- 3x + y - 2z = - 1


linear system 3 variables show help again

Answer 1

x = 3

y = 2

z = -3

Explanation:

L1 x + 2y + z = 4

L2 2x - y + 4z = - 8

L3 - 3x + y - 2z = - 1

2L1 - L2

2x + 4y + 2z = 8

-2x + y - 4z = 8

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5y - 2z = 16 L4

3L1 + L3

3x + 6y + 3z = 12

-3x + y - 2z = -1

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7y + z = 11 L5

L4 + 2L5

5y - 2z = 16

14y + 2z = 22

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19y = 38

y = 38 / 19

y = 2

7y + z = 11

7(2) + z = 11

14 + z = 11

z = 11 - 14

z = -3

x + 2y + z = 4

x + 2(2) + (-3) = 4

x + 4 - 3 = 4

x + 1 = 4

x = 4 - 1

x = 3