Question

Solve the following equation using Gaussian elimination method


`m + 2n + 2p = 4 \\ 3m - n + 4p = 25 \\ 3m + 2n - p = - 4`
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Answer 1

Eliminate p :

2 (m + 2n + 2p) + (-1) (3m - n + 4p) = 2 (4) + (-1) 25

2m + 4n + 4p - 3m + n - 4p = 8 - 25

-m + 5n = -17

(m + 2n + 2p) + 2 (3m + 2n - p) = 4 + 2 (-4)

m + 2n + 2p + 6m + 4n - 2p = 4 - 8

7m + 6n = -4

Eliminate m :

7 (-m + 5n) + (7m + 6n) = 7 (-17) + (-4)

-7m + 35n + 7m + 6n = -119 - 4

41n = -123

Solve for n :

n = -3

Solve for m :

-m + 5 (-3) = -17

-m - 15 = -17

m = 2

Solve for p :

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

2 - 6 + 2p = 4

2p = 8

p = 4