Solve {l}{3x-2y+8t=3}{6x-3y+2t=6}{9x-11+6t=8}

$$\left. \begin{array} { l } { 3 x - 2 y + 8 t = 3 } \\ { 6 x - 3 y + 2 t = 6 } \\ { 9 x - 11 + 6 t = 8 } \end{array} \right.$$

Solve for x, y, t

$$x = \frac{199}{99} = 2\frac{1}{99} \approx 2.01010101$$

$$y = \frac{70}{33} = 2\frac{4}{33} \approx 2.121212121$$

$$t=\frac{5}{33}\approx 0.151515152$$

Short Steps Using Substitution

Solve 3x-2y+8t=3 for x.

$$x=\frac{2}{3}y-\frac{8}{3}t+1$$

Substitute \frac{2}{3}y-\frac{8}{3}t+1 for x in the second and third equation.

$$6\left(\frac{2}{3}y-\frac{8}{3}t+1\right)-3y+2t=6 9\left(\frac{2}{3}y-\frac{8}{3}t+1\right)-11+6t=8$$

Solve these equations for y and t respectively.

$$y=14t t=-\frac{5}{9}+\frac{1}{3}y$$

Substitute 14t for y in the equation t=-\frac{5}{9}+\frac{1}{3}y.

$$t=-\frac{5}{9}+\frac{1}{3}\times 14t$$

Solve t=-\frac{5}{9}+\frac{1}{3}\times 14t for t.

$$t=\frac{5}{33}$$

Substitute \frac{5}{33} for t in the equation y=14t.

$$y=14\times \frac{5}{33}$$

Calculate y from y=14\times \frac{5}{33}.

$$y=\frac{70}{33}$$

Substitute \frac{70}{33} for y and \frac{5}{33} for t in the equation x=\frac{2}{3}y-\frac{8}{3}t+1.

$$x=\frac{2}{3}\times \frac{70}{33}-\frac{8}{3}\times \frac{5}{33}+1$$

Calculate x from x=\frac{2}{3}\times \frac{70}{33}-\frac{8}{3}\times \frac{5}{33}+1.

$$x=\frac{199}{99}$$

The system is now solved.

$$x=\frac{199}{99} y=\frac{70}{33} t=\frac{5}{33}$$