Question

x+2y +z = 2
3x+8y+z=12
4y+z=2​

Answer 1

Método: Sustitución

{x + 2y + z = 2

{3x + 8y + z = 12

{4y + z = 2

{x + 2y + z = 2

{3x + 8y + z = 12

{y = 1/2 - 1/4z

{x + 2(1/2 - 1/4z) + z = 2

{3x + 8(1/2 - 1/4z) + z = 12

{2x + z = 2

{3x - z = 8

Resolvemos para x...

2x + z + 3x - z = 2 + 8

2x + 3x = 2 + 8

5x = 2 + 8

5x = 10

x = 2

Resolver para z...

2 × 2 + z = 2

4 + z = 2

z = 2 - 4

z = -2

Resolver para y...

y = 1/2 - 1/4 × (-2)

y = 1/2 + 1/4 × 2

y = 1/2 + 1/2

y = 1

(x, y, z) = (2, 1, -2)

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