Solve {c}{x+y=z}{6.37x+8z=5}{3y+8z=-15}

$$\left. \begin{array} { c } { x + y = z } \\ { 6.37 x + 8 z = 5 } \\ { 3 y + 8 z = - 15 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{17500}{9407} = 1\frac{8093}{9407} \approx 1.860316785$$

$$y = -\frac{25555}{9407} = -2\frac{6741}{9407} \approx -2.716594026$$

$$z=-\frac{8055}{9407}\approx -0.85627724$$

Short Steps Using Substitution

Solve x+y=z for z.

$$z=x+y$$

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

$$6.37x+8\left(x+y\right)=5 3y+8\left(x+y\right)=-15$$

Solve these equations for y and x respectively.

$$y=-\frac{1437}{800}x+\frac{5}{8} x=-\frac{15}{8}-\frac{11}{8}y$$

Substitute -\frac{1437}{800}x+\frac{5}{8} for y in the equation x=-\frac{15}{8}-\frac{11}{8}y.

$$x=-\frac{15}{8}-\frac{11}{8}\left(-\frac{1437}{800}x+\frac{5}{8}\right)$$

Solve x=-\frac{15}{8}-\frac{11}{8}\left(-\frac{1437}{800}x+\frac{5}{8}\right) for x.

$$x=\frac{17500}{9407}$$

Substitute \frac{17500}{9407} for x in the equation y=-\frac{1437}{800}x+\frac{5}{8}.

$$y=-\frac{1437}{800}\times \frac{17500}{9407}+\frac{5}{8}$$

Calculate y from y=-\frac{1437}{800}\times \frac{17500}{9407}+\frac{5}{8}.

$$y=-\frac{25555}{9407}$$

Substitute -\frac{25555}{9407} for y and \frac{17500}{9407} for x in the equation z=x+y.

$$z=\frac{17500}{9407}-\frac{25555}{9407}$$

Calculate z from z=\frac{17500}{9407}-\frac{25555}{9407}.

$$z=-\frac{8055}{9407}$$

The system is now solved.

$$x=\frac{17500}{9407} y=-\frac{25555}{9407} z=-\frac{8055}{9407}$$