Solve {c}{6x-4y-4=-4}{-4x+13y=4-3u}{u=2(2-x)}

$$\left. \begin{array} { c } { 6 x - 4 y - 4 = - 4 } \\ { - 4 x + 13 y = 4 - 3 u } \\ { u = 2 ( 2 - x ) } \end{array} \right.$$

Solve for x, y, u

$$x=-\frac{16}{19}\approx -0.842105263$$

$$y = -\frac{24}{19} = -1\frac{5}{19} \approx -1.263157895$$

$$u = \frac{108}{19} = 5\frac{13}{19} \approx 5.684210526$$

Short Steps Using Substitution

Reorder the equations.

$$u=2\left(2-x\right) -4x+13y=4-3u 6x-4y-4=-4$$

Calculate u from u=2\left(2-x\right).

$$u=4-2x$$

Substitute 4-2x for u in the equation -4x+13y=4-3u.

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

Solve the second equation for y and the third equation for x.

$$y=-\frac{8}{13}+\frac{10}{13}x x=\frac{2}{3}y$$

Substitute -\frac{8}{13}+\frac{10}{13}x for y in the equation x=\frac{2}{3}y.

$$x=\frac{2}{3}\left(-\frac{8}{13}+\frac{10}{13}x\right)$$

Solve x=\frac{2}{3}\left(-\frac{8}{13}+\frac{10}{13}x\right) for x.

$$x=-\frac{16}{19}$$

Substitute -\frac{16}{19} for x in the equation y=-\frac{8}{13}+\frac{10}{13}x.

$$y=-\frac{8}{13}+\frac{10}{13}\left(-\frac{16}{19}\right)$$

Calculate y from y=-\frac{8}{13}+\frac{10}{13}\left(-\frac{16}{19}\right).

$$y=-\frac{24}{19}$$

Substitute -\frac{16}{19} for x in the equation u=4-2x.

$$u=4-2\left(-\frac{16}{19}\right)$$

Calculate u from u=4-2\left(-\frac{16}{19}\right).

$$u=\frac{108}{19}$$

The system is now solved.

$$x=-\frac{16}{19} y=-\frac{24}{19} u=\frac{108}{19}$$