Me dicen la solución de este sistema de ecuaciones x - y + z = 0 2x - 4y + z = 3 - 3x + 3y + z = 12?

<img src="https://tex.z-dn.net/?f=x-y%2Bz%3D0%20%5C%5C%20" />

Multiplicando a 2x - 4y + z = 3 por - 1 para sumarlo a la ecuacion anterior :

<img src="https://tex.z-dn.net/?f=%20%20%20%5Chspace%7B4mm%7Dx%5Chspace%7B2mm%7D-y%5Chspace%7B1mm%7D%2Bz%3D0%20%20%5C%5C%20%0A-2x%2B4y-z%3D-3%20%5C%5C%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%20%5C%5C%20-x%5Chspace%7B2mm%7D%2B3y%5Chspace%7B5mm%7D%3D-3%0A" />

Sumando - 2x + 4y - z = - 3 a la tercera ecuacion :

<img src="https://tex.z-dn.net/?f=%5Chspace%7B2mm%7D-3x%5Chspace%7B2mm%7D%2B3y%5Chspace%7B1mm%7D%2Bz%3D12%5C%5C%20-2x%2B4y-z%3D-3%20%5C%5C%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%20%5C%5C%20-5x%5Chspace%7B2mm%7D%2B7y%5Chspace%7B5mm%7D%3D9%0A" />

Multiplicando por - 5 a - x + 3y = - 3 para sumarlo a - 5x + 7y = 9

<img src="https://tex.z-dn.net/?f=5x%5Chspace%7B2mm%7D-15y%5Chspace%7B1mm%7D%3D15%5C%5C%205x%5Chspace%7B2mm%7D%2B7y%5Chspace%7B3mm%7D%3D9%5C%5C%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%20%5C%5C%20%20%5Chspace%7B2mm%7D-8y%5Chspace%7B5mm%7D%3D24%20%5C%5C%20%20%20%5C%5C%20y%3D%20%5Cfrac%7B24%7D%7B-8%7D%20%3D-3%20%5C%5C%20%20%5C%5C%20-5x%2B7y%3D9%20%5C%5C%20-5x%2B7%28-3%29%3D9%20%5C%5C%20-5x-21%3D9%20%5C%5C-%205x%3D30%20%5C%5C%20x%3D-6%0A%20%5C%5C%20%20%5C%5C%20x-y%2Bz%3D0%20%5C%5C%20-6-%28-3%29%2Bz%3D0%20%5C%5C%20-6%2B3%2Bz%3D0%20%5C%5C%20z-3%3D0%20%5C%5C%20z%3D3%20%5C%5C%20%20%5C%5C%20x%3D-6%20%5C%5C%20y%3D-3%20%5C%5C%20z%3D3" />.