Question

resolva o sistema
x+2y-z=9
2x+y-z=3
3x-y-2z=-4

Answer 1

x = 9 - 2y + z

z = 2x + y - 3

y = 3x - 2z + 4

z = 2 * (9 - 2y + z) + y - 3
z = 18 - 4y + 2z + y - 3
z = 15 - 3y + 2z
3y = 15 + z
3 * (3x - 2z + 4) = 15 + z
9x - 6z + 12 = 15 + z
9x = 3 + 7z

x = 9 - 2*(3x - 2z + 4) + z
x = 9 - 6x + 4z + z
7x = 9 + 5z
x = (9 + 5z)/7

9 * (9 + 5z)/7 = 3 + 7z
(81 + 45z)/7 = 3 + 7z
81 + 45z = (3 + 7z) * 7
81 + 45z = 21 + 49z
60 = 4z
z = 60/4
z = 15

9x = 3 + 7z
9x = 3 + 7 * 15
9x = 3 + 105
9x = 108
x = 108/9
x = 12

y = 3x - 2z + 4
y = 3 * 12 - 2 * 15 + 4
y = 36 - 30 + 4
y = 6 + 4
y = 10

Resposta:
y = 10
x = 12
z = 15