Solve {l}{a=2b+c}{b=3c}{a=c/2}

$$\left. \begin{array} { l } { a = 2 b + c } \\ { b = 3 c } \\ { a = c / 2 } \end{array} \right.$$

Solve for a, b, c

$$a=0$$

$$b=0$$

$$c=0$$

Short Steps Using Substitution

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

$$a=2b+c b=3c 2a=c$$

Substitute 2b+c for a in the equation 2a=c.

$$2\left(2b+c\right)=c$$

Solve 2\left(2b+c\right)=c for c.

$$c=-4b$$

Substitute 3c for b in the equation c=-4b.

$$c=-4\times 3c$$

Solve c=-4\times 3c for c.

$$c=0$$

Substitute 0 for c in the equation b=3c.

$$b=3\times 0$$

Calculate b from b=3\times 0.

$$b=0$$

Substitute 0 for b and 0 for c in the equation a=2b+c.

$$a=2\times 0+0$$

Calculate a from a=2\times 0+0.

$$a=0$$

The system is now solved.

$$a=0 b=0 c=0$$