Resolver {l}{5x+3y-z=6}{4x+5y-10z=4}{2x+8y-3z=2}

$$\left. \begin{array}{l}{ 5 x + 3 y - z = 6 }\\{ 4 x + 5 y - 10 z = 4 }\\{ 2 x + 8 y - 3 z = 2 }\end{array} \right.$$

Resolver x, y, z

$$x = \frac{344}{279} = 1\frac{65}{279} \approx 1.23297491$$

$$y=-\frac{8}{279}\approx -0.028673835$$

$$z=\frac{22}{279}\approx 0.078853047$$

Pasos breves que usan substitución

Despexa z en 5x+3y-z=6.

$$z=5x+3y-6$$

Substitúe 5x+3y-6 por z na segunda e na terceira ecuación.

$$4x+5y-10\left(5x+3y-6\right)=4 2x+8y-3\left(5x+3y-6\right)=2$$

Despexa y e x respectivamente nestas ecuacións.

$$y=\frac{56}{25}-\frac{46}{25}x x=-\frac{1}{13}y+\frac{16}{13}$$

Substitúe y por \frac{56}{25}-\frac{46}{25}x na ecuación x=-\frac{1}{13}y+\frac{16}{13}.

$$x=-\frac{1}{13}\left(\frac{56}{25}-\frac{46}{25}x\right)+\frac{16}{13}$$

Despexa x en x=-\frac{1}{13}\left(\frac{56}{25}-\frac{46}{25}x\right)+\frac{16}{13}.

$$x=\frac{344}{279}$$

Substitúe x por \frac{344}{279} na ecuación y=\frac{56}{25}-\frac{46}{25}x.

$$y=\frac{56}{25}-\frac{46}{25}\times \frac{344}{279}$$

Calcular y tendo en conta que y=\frac{56}{25}-\frac{46}{25}\times \frac{344}{279}.

$$y=-\frac{8}{279}$$

Substitúe -\frac{8}{279} por y e \frac{344}{279} por x na ecuación z=5x+3y-6.

$$z=5\times \frac{344}{279}+3\left(-\frac{8}{279}\right)-6$$

Calcular z tendo en conta que z=5\times \frac{344}{279}+3\left(-\frac{8}{279}\right)-6.

$$z=\frac{22}{279}$$

O sistema xa funciona correctamente.

$$x=\frac{344}{279} y=-\frac{8}{279} z=\frac{22}{279}$$