Solve {l}{0=4-4t-3x}{0=3t+x}{z=-2t-3x}

$$\left\{ \begin{array} { l } { 0 = 4 - 4 t - 3 x } \\ { 0 = 3 t + x } \\ { z = - 2 t - 3 x } \end{array} \right.$$

Solve for t, x, z

$$x = \frac{12}{5} = 2\frac{2}{5} = 2.4$$

$$z = -\frac{28}{5} = -5\frac{3}{5} = -5.6$$

$$t=-\frac{4}{5}=-0.8$$

Short Steps Using Substitution

Reorder the equations.

$$0=3t+x 0=4-4t-3x z=-2t-3x$$

Solve 0=3t+x for x.

$$x=-3t$$

Substitute -3t for x in the second and third equation.

$$0=4-4t-3\left(-3\right)t z=-2t-3\left(-3\right)t$$

Solve these equations for t and z respectively.

$$t=-\frac{4}{5} z=7t$$

Substitute -\frac{4}{5} for t in the equation z=7t.

$$z=7\left(-\frac{4}{5}\right)$$

Calculate z from z=7\left(-\frac{4}{5}\right).

$$z=-\frac{28}{5}$$

Substitute -\frac{4}{5} for t in the equation x=-3t.

$$x=-3\left(-\frac{4}{5}\right)$$

Calculate x from x=-3\left(-\frac{4}{5}\right).

$$x=\frac{12}{5}$$

The system is now solved.

$$t=-\frac{4}{5} x=\frac{12}{5} z=-\frac{28}{5}$$