Solve {l}{7x+y+z=9}{9y+z-x=6}{z-x-y=19}

$$\left. \begin{array} { l } { 7 x + y + z = 9 } \\ { 9 y + z - x = 6 } \\ { z - x - y = 19 } \end{array} \right.$$

Solve for x, y, z

$$x=-\frac{37}{40}=-0.925$$

$$y = -\frac{13}{10} = -1\frac{3}{10} = -1.3$$

$$z = \frac{671}{40} = 16\frac{31}{40} = 16.775$$

Short Steps Using Substitution

Solve 7x+y+z=9 for y.

$$y=-7x-z+9$$

Substitute -7x-z+9 for y in the second and third equation.

$$9\left(-7x-z+9\right)+z-x=6 z-x-\left(-7x-z+9\right)=19$$

Solve these equations for x and z respectively.

$$x=-\frac{1}{8}z+\frac{75}{64} z=14-3x$$

Substitute -\frac{1}{8}z+\frac{75}{64} for x in the equation z=14-3x.

$$z=14-3\left(-\frac{1}{8}z+\frac{75}{64}\right)$$

Solve z=14-3\left(-\frac{1}{8}z+\frac{75}{64}\right) for z.

$$z=\frac{671}{40}$$

Substitute \frac{671}{40} for z in the equation x=-\frac{1}{8}z+\frac{75}{64}.

$$x=-\frac{1}{8}\times \frac{671}{40}+\frac{75}{64}$$

Calculate x from x=-\frac{1}{8}\times \frac{671}{40}+\frac{75}{64}.

$$x=-\frac{37}{40}$$

Substitute -\frac{37}{40} for x and \frac{671}{40} for z in the equation y=-7x-z+9.

$$y=-7\left(-\frac{37}{40}\right)-\frac{671}{40}+9$$

Calculate y from y=-7\left(-\frac{37}{40}\right)-\frac{671}{40}+9.

$$y=-\frac{13}{10}$$

The system is now solved.

$$x=-\frac{37}{40} y=-\frac{13}{10} z=\frac{671}{40}$$