Solve {c}{3x-2y+z=2}{4x+8y-10z=4}{2x+6y+4z=8}

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

Solve for x, y, z

$$x=\frac{84}{89}\approx 0.943820225$$

$$y=\frac{60}{89}\approx 0.674157303$$

$$z=\frac{46}{89}\approx 0.516853933$$

Short Steps Using Substitution

Solve 3x-2y+z=2 for z.

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

Substitute -3x+2y+2 for z in the second and third equation.

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

Solve these equations for y and x respectively.

$$y=-2+\frac{17}{6}x x=\frac{7}{5}y$$

Substitute -2+\frac{17}{6}x for y in the equation x=\frac{7}{5}y.

$$x=\frac{7}{5}\left(-2+\frac{17}{6}x\right)$$

Solve x=\frac{7}{5}\left(-2+\frac{17}{6}x\right) for x.

$$x=\frac{84}{89}$$

Substitute \frac{84}{89} for x in the equation y=-2+\frac{17}{6}x.

$$y=-2+\frac{17}{6}\times \frac{84}{89}$$

Calculate y from y=-2+\frac{17}{6}\times \frac{84}{89}.

$$y=\frac{60}{89}$$

Substitute \frac{60}{89} for y and \frac{84}{89} for x in the equation z=-3x+2y+2.

$$z=-3\times \frac{84}{89}+2\times \frac{60}{89}+2$$

Calculate z from z=-3\times \frac{84}{89}+2\times \frac{60}{89}+2.

$$z=\frac{46}{89}$$

The system is now solved.

$$x=\frac{84}{89} y=\frac{60}{89} z=\frac{46}{89}$$