Solve {l}{2x-4y+z=0}{3x-y-2z-4=0}{x=2}

$$\left\{ \begin{array} { l } { 2 x - 4 y + z = 0 } \\ { 3 x - y - 2 z - 4 = 0 } \\ { x = 2 } \end{array} \right.$$

Solve for x, y, z

$$x=2$$

$$y = \frac{10}{9} = 1\frac{1}{9} \approx 1.111111111$$

$$z=\frac{4}{9}\approx 0.444444444$$

Short Steps Using Substitution

Reorder the equations.

$$x=2 3x-y-2z-4=0 2x-4y+z=0$$

Substitute 2 for x in the second and third equation.

$$3\times 2-y-2z-4=0 2\times 2-4y+z=0$$

Solve these equations for y and z respectively.

$$y=2-2z z=-4+4y$$

Substitute 2-2z for y in the equation z=-4+4y.

$$z=-4+4\left(2-2z\right)$$

Solve z=-4+4\left(2-2z\right) for z.

$$z=\frac{4}{9}$$

Substitute \frac{4}{9} for z in the equation y=2-2z.

$$y=2-2\times \frac{4}{9}$$

Calculate y from y=2-2\times \frac{4}{9}.

$$y=\frac{10}{9}$$

The system is now solved.

$$x=2 y=\frac{10}{9} z=\frac{4}{9}$$