Solve {l}{2x+3y-z=-4}{3x+2y+2z=14}{x=-13}

$$\left. \begin{array}{l}{ 2 x + 3 y - z = - 4 }\\{ 3 x + 2 y + 2 z = 14 }\\{ x = - 13 }\end{array} \right.$$

Solve for x, y, z

$$x=-13$$

$$y = \frac{97}{8} = 12\frac{1}{8} = 12.125$$

$$z = \frac{115}{8} = 14\frac{3}{8} = 14.375$$

Short Steps Using Substitution

Reorder the equations.

$$x=-13 3x+2y+2z=14 2x+3y-z=-4$$

Substitute -13 for x in the second and third equation.

$$3\left(-13\right)+2y+2z=14 2\left(-13\right)+3y-z=-4$$

Solve these equations for y and z respectively.

$$y=\frac{53}{2}-z z=-22+3y$$

Substitute \frac{53}{2}-z for y in the equation z=-22+3y.

$$z=-22+3\left(\frac{53}{2}-z\right)$$

Solve z=-22+3\left(\frac{53}{2}-z\right) for z.

$$z=\frac{115}{8}$$

Substitute \frac{115}{8} for z in the equation y=\frac{53}{2}-z.

$$y=\frac{53}{2}-\frac{115}{8}$$

Calculate y from y=\frac{53}{2}-\frac{115}{8}.

$$y=\frac{97}{8}$$

The system is now solved.

$$x=-13 y=\frac{97}{8} z=\frac{115}{8}$$