Solve {l}{2x+3y+z=7}{536x-2y-z=-74}{3x+y-z=7}

$$\left. \begin{array} { l } { 2 x + 3 y + z = 7 } \\ { 536 x - 2 y - z = - 74 } \\ { 3 x + y - z = 7 } \end{array} \right.$$

Solve for x, y, z

$$x=-\frac{282}{2147}\approx -0.131346064$$

$$y = \frac{7867}{2147} = 3\frac{1426}{2147} \approx 3.66418258$$

$$z = -\frac{8008}{2147} = -3\frac{1567}{2147} \approx -3.729855612$$

Short Steps Using Substitution

Solve 2x+3y+z=7 for z.

$$z=-2x-3y+7$$

Substitute -2x-3y+7 for z in the second and third equation.

$$536x-2y-\left(-2x-3y+7\right)=-74 3x+y-\left(-2x-3y+7\right)=7$$

Solve these equations for y and x respectively.

$$y=-538x-67 x=\frac{14}{5}-\frac{4}{5}y$$

Substitute -538x-67 for y in the equation x=\frac{14}{5}-\frac{4}{5}y.

$$x=\frac{14}{5}-\frac{4}{5}\left(-538x-67\right)$$

Solve x=\frac{14}{5}-\frac{4}{5}\left(-538x-67\right) for x.

$$x=-\frac{282}{2147}$$

Substitute -\frac{282}{2147} for x in the equation y=-538x-67.

$$y=-538\left(-\frac{282}{2147}\right)-67$$

Calculate y from y=-538\left(-\frac{282}{2147}\right)-67.

$$y=\frac{7867}{2147}$$

Substitute \frac{7867}{2147} for y and -\frac{282}{2147} for x in the equation z=-2x-3y+7.

$$z=-2\left(-\frac{282}{2147}\right)-3\times \frac{7867}{2147}+7$$

Calculate z from z=-2\left(-\frac{282}{2147}\right)-3\times \frac{7867}{2147}+7.

$$z=-\frac{8008}{2147}$$

The system is now solved.

$$x=-\frac{282}{2147} y=\frac{7867}{2147} z=-\frac{8008}{2147}$$