Solve {l}{314151y=x}{y=5+z}{z=x-y}

$$\left\{ \begin{array} { l } { 314151 y = x } \\ { y = 5 + z } \\ { z = x - y } \end{array} \right.$$

Solve for y, x, z

$$x = -\frac{1570755}{314149} = -5\frac{10}{314149} \approx -5.000031832$$

$$y=-\frac{5}{314149}\approx -0.000015916$$

$$z = -\frac{1570750}{314149} = -5\frac{5}{314149} \approx -5.000015916$$

Short Steps Using Substitution

Solve 314151y=x for x.

$$x=314151y$$

Substitute 314151y for x in the equation z=x-y.

$$z=314151y-y$$

Solve z=314151y-y for z.

$$z=314150y$$

Substitute 5+z for y in the equation z=314150y.

$$z=314150\left(5+z\right)$$

Solve z=314150\left(5+z\right) for z.

$$z=-\frac{1570750}{314149}$$

Substitute -\frac{1570750}{314149} for z in the equation y=5+z.

$$y=5-\frac{1570750}{314149}$$

Calculate y from y=5-\frac{1570750}{314149}.

$$y=-\frac{5}{314149}$$

Substitute -\frac{5}{314149} for y in the equation x=314151y.

$$x=314151\left(-\frac{5}{314149}\right)$$

Calculate x from x=314151\left(-\frac{5}{314149}\right).

$$x=-\frac{1570755}{314149}$$

The system is now solved.

$$y=-\frac{5}{314149} x=-\frac{1570755}{314149} z=-\frac{1570750}{314149}$$