Question

matemática
x-y+2z=1
3×+y-z=2
5x-y+3z=1​

Answer 1

Resposta:

x = 6/7, y = 2,  z = -3/7

Explicação passo a passo:

x-y+2z=1

3×+y-z=2

5x-y+3z=1​

x-y+2z=1

3×+y-z=2

4x + z = 3

z = 3 - 4x

x-y+2z=1

3×+y-z=2 (-2)

5x-y+3z=1

x-y+2z=1

-6×-2y+2z=-4

5x-y+3z=1

-4y + 7z = -2

-4y = -2 - 7x (-)

4y = 2 + 7x

y = (2+7x)/4

x - ((2+7x/4) + 2(3-4x) = 1

x - (2 -7x)/4 + 6 - 8x = 1

4x - 2 - 7x + 24 - 32x = 4

11x - 32x = 4 - 22

21x = 18

x = 18/21

x = 6/7

y = (2+7x)/4

y = (2 +  7 * 6/7)/4

y = (2 + 42/7)/4

y = (2 + 6)/4

y = 8/4

y = 2

z = 3 - 4x

z = 3 - 4 * 6/7

z = 3 - 24/7

z = -3/7

Prova:

5x-y+3z=1​

5 * 6/7 - 2 + 3 * -3/7 = 1

30/7 - 2 - 9/7 = 1

30 - 14 - 9 = 7

30 - 23 = 7

7 = 7

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