Solve {l}{a+x=6}{b+x=0}{b=-3-a}

$$\left\{ \begin{array} { l } { a + x = 6 } \\ { b + x = 0 } \\ { b = - 3 - a } \end{array} \right.$$

Solve for a, x, b

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

$$a = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$b = -\frac{9}{2} = -4\frac{1}{2} = -4.5$$

Short Steps Using Substitution

Reorder the equations.

$$b=-3-a b+x=0 a+x=6$$

Substitute -3-a for b in the equation b+x=0.

$$-3-a+x=0$$

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

$$x=3+a a=-x+6$$

Substitute 3+a for x in the equation a=-x+6.

$$a=-\left(3+a\right)+6$$

Solve a=-\left(3+a\right)+6 for a.

$$a=\frac{3}{2}$$

Substitute \frac{3}{2} for a in the equation x=3+a.

$$x=3+\frac{3}{2}$$

Calculate x from x=3+\frac{3}{2}.

$$x=\frac{9}{2}$$

Substitute \frac{3}{2} for a in the equation b=-3-a.

$$b=-3-\frac{3}{2}$$

Calculate b from b=-3-\frac{3}{2}.

$$b=-\frac{9}{2}$$

The system is now solved.

$$a=\frac{3}{2} x=\frac{9}{2} b=-\frac{9}{2}$$