Solve {c}{4x-y+3z-6=0}{x+5y-z+10=0}{x=10}

$$\left. \begin{array} { c } { 4 x - y + 3 z - 6 = 0 } \\ { x + 5 y - z + 10 = 0 } \\ { x = 10 } \end{array} \right.$$

Solve for x, y, z

$$x=10$$

$$y = -\frac{47}{7} = -6\frac{5}{7} \approx -6.714285714$$

$$z = -\frac{95}{7} = -13\frac{4}{7} \approx -13.571428571$$

Short Steps Using Substitution

Reorder the equations.

$$x=10 x+5y-z+10=0 4x-y+3z-6=0$$

Substitute 10 for x in the second and third equation.

$$10+5y-z+10=0 4\times 10-y+3z-6=0$$

Solve these equations for y and z respectively.

$$y=-4+\frac{1}{5}z z=-\frac{34}{3}+\frac{1}{3}y$$

Substitute -4+\frac{1}{5}z for y in the equation z=-\frac{34}{3}+\frac{1}{3}y.

$$z=-\frac{34}{3}+\frac{1}{3}\left(-4+\frac{1}{5}z\right)$$

Solve z=-\frac{34}{3}+\frac{1}{3}\left(-4+\frac{1}{5}z\right) for z.

$$z=-\frac{95}{7}$$

Substitute -\frac{95}{7} for z in the equation y=-4+\frac{1}{5}z.

$$y=-4+\frac{1}{5}\left(-\frac{95}{7}\right)$$

Calculate y from y=-4+\frac{1}{5}\left(-\frac{95}{7}\right).

$$y=-\frac{47}{7}$$

The system is now solved.

$$x=10 y=-\frac{47}{7} z=-\frac{95}{7}$$