Solve {l}{a=b+c}{c=a/2}{b=4}

$$\left. \begin{array} { l } { a = b + c } \\ { c = \frac { a } { 2 } } \\ { b = 4 } \end{array} \right.$$

Solve for a, b, c

$$a=8$$

$$b=4$$

$$c=4$$

Short Steps Using Substitution

Multiply each equation by the least common multiple of denominators in it. Simplify.

$$a=b+c 2c=a b=4$$

Reorder the equations.

$$b=4 2c=a a=b+c$$

Substitute 4 for b in the equation a=b+c.

$$a=4+c$$

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

$$a=2c c=a-4$$

Substitute 2c for a in the equation c=a-4.

$$c=2c-4$$

Solve c=2c-4 for c.

$$c=4$$

Substitute 4 for c in the equation a=2c.

$$a=2\times 4$$

Calculate a from a=2\times 4.

$$a=8$$

The system is now solved.

$$a=8 b=4 c=4$$