Solve {l}{8x+3y-4+3z=0}{2y+3x+1-2z=0}{3x-2y-5=0}

$$\left\{ \begin{array} { l } { 8 x + 3 y - 4 + 3 z = 0 } \\ { 2 y + 3 x + 1 - 2 z = 0 } \\ { 3 x - 2 y - 5 = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{35}{43}\approx 0.813953488$$

$$y = -\frac{55}{43} = -1\frac{12}{43} \approx -1.279069767$$

$$z=\frac{19}{43}\approx 0.441860465$$

Short Steps Using Substitution

Solve 8x+3y-4+3z=0 for x.

$$x=-\frac{3}{8}y+\frac{1}{2}-\frac{3}{8}z$$

Substitute -\frac{3}{8}y+\frac{1}{2}-\frac{3}{8}z for x in the second and third equation.

$$2y+3\left(-\frac{3}{8}y+\frac{1}{2}-\frac{3}{8}z\right)+1-2z=0 3\left(-\frac{3}{8}y+\frac{1}{2}-\frac{3}{8}z\right)-2y-5=0$$

Solve these equations for y and z respectively.

$$y=-\frac{20}{7}+\frac{25}{7}z z=-\frac{28}{9}-\frac{25}{9}y$$

Substitute -\frac{20}{7}+\frac{25}{7}z for y in the equation z=-\frac{28}{9}-\frac{25}{9}y.

$$z=-\frac{28}{9}-\frac{25}{9}\left(-\frac{20}{7}+\frac{25}{7}z\right)$$

Solve z=-\frac{28}{9}-\frac{25}{9}\left(-\frac{20}{7}+\frac{25}{7}z\right) for z.

$$z=\frac{19}{43}$$

Substitute \frac{19}{43} for z in the equation y=-\frac{20}{7}+\frac{25}{7}z.

$$y=-\frac{20}{7}+\frac{25}{7}\times \frac{19}{43}$$

Calculate y from y=-\frac{20}{7}+\frac{25}{7}\times \frac{19}{43}.

$$y=-\frac{55}{43}$$

Substitute -\frac{55}{43} for y and \frac{19}{43} for z in the equation x=-\frac{3}{8}y+\frac{1}{2}-\frac{3}{8}z.

$$x=-\frac{3}{8}\left(-\frac{55}{43}\right)+\frac{1}{2}-\frac{3}{8}\times \frac{19}{43}$$

Calculate x from x=-\frac{3}{8}\left(-\frac{55}{43}\right)+\frac{1}{2}-\frac{3}{8}\times \frac{19}{43}.

$$x=\frac{35}{43}$$

The system is now solved.

$$x=\frac{35}{43} y=-\frac{55}{43} z=\frac{19}{43}$$