Solve {l}{x+y=8}{3x-y-a=0}{x+2y+a+3=0}

$$\left\{ \begin{array} { l } { x + y = 8 } \\ { 3 x - y - a = 0 } \\ { x + 2 y + a + 3 = 0 } \end{array} \right.$$

Solve for x, y, a

$$x = -\frac{11}{3} = -3\frac{2}{3} \approx -3.666666667$$

$$y = \frac{35}{3} = 11\frac{2}{3} \approx 11.666666667$$

$$a = -\frac{68}{3} = -22\frac{2}{3} \approx -22.666666667$$

Short Steps Using Substitution

Solve x+y=8 for x.

$$x=-y+8$$

Substitute -y+8 for x in the second and third equation.

$$3\left(-y+8\right)-y-a=0 -y+8+2y+a+3=0$$

Solve these equations for y and a respectively.

$$y=6-\frac{1}{4}a a=-y-11$$

Substitute 6-\frac{1}{4}a for y in the equation a=-y-11.

$$a=-\left(6-\frac{1}{4}a\right)-11$$

Solve a=-\left(6-\frac{1}{4}a\right)-11 for a.

$$a=-\frac{68}{3}$$

Substitute -\frac{68}{3} for a in the equation y=6-\frac{1}{4}a.

$$y=6-\frac{1}{4}\left(-\frac{68}{3}\right)$$

Calculate y from y=6-\frac{1}{4}\left(-\frac{68}{3}\right).

$$y=\frac{35}{3}$$

Substitute \frac{35}{3} for y in the equation x=-y+8.

$$x=-\frac{35}{3}+8$$

Calculate x from x=-\frac{35}{3}+8.

$$x=-\frac{11}{3}$$

The system is now solved.

$$x=-\frac{11}{3} y=\frac{35}{3} a=-\frac{68}{3}$$