Solve {l}{2x+4y-12z=6}{x+y+2z=26}{3x-3y+3z=3}

$$\left. \begin{array} { l } { 2 x + 4 y - 12 z = 6 } \\ { x + y + 2 z = 26 } \\ { 3 x - 3 y + 3 z = 3 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{123}{17} = 7\frac{4}{17} \approx 7.235294118$$

$$y = \frac{177}{17} = 10\frac{7}{17} \approx 10.411764706$$

$$z = \frac{71}{17} = 4\frac{3}{17} \approx 4.176470588$$

Short Steps Using Substitution

Reorder the equations.

$$x+y+2z=26 2x+4y-12z=6 3x-3y+3z=3$$

Solve x+y+2z=26 for x.

$$x=-y-2z+26$$

Substitute -y-2z+26 for x in the second and third equation.

$$2\left(-y-2z+26\right)+4y-12z=6 3\left(-y-2z+26\right)-3y+3z=3$$

Solve these equations for y and z respectively.

$$y=-23+8z z=25-2y$$

Substitute -23+8z for y in the equation z=25-2y.

$$z=25-2\left(-23+8z\right)$$

Solve z=25-2\left(-23+8z\right) for z.

$$z=\frac{71}{17}$$

Substitute \frac{71}{17} for z in the equation y=-23+8z.

$$y=-23+8\times \frac{71}{17}$$

Calculate y from y=-23+8\times \frac{71}{17}.

$$y=\frac{177}{17}$$

Substitute \frac{177}{17} for y and \frac{71}{17} for z in the equation x=-y-2z+26.

$$x=-\frac{177}{17}-2\times \frac{71}{17}+26$$

Calculate x from x=-\frac{177}{17}-2\times \frac{71}{17}+26.

$$x=\frac{123}{17}$$

The system is now solved.

$$x=\frac{123}{17} y=\frac{177}{17} z=\frac{71}{17}$$