Solve {c}{A+B=2}{A+C=2B}{C=2A}

$$\left. \begin{array} { c } { A + B = 2 } \\ { A + C = 2 B } \\ { C = 2 A } \end{array} \right.$$

Solve for A, B, C

$$A=\frac{4}{5}=0.8$$

$$B = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

$$C = \frac{8}{5} = 1\frac{3}{5} = 1.6$$

Short Steps Using Substitution

Reorder the equations.

$$C=2A A+C=2B A+B=2$$

Substitute 2A for C in the equation A+C=2B.

$$A+2A=2B$$

Solve the second equation for B and the third equation for A.

$$B=\frac{3}{2}A A=-B+2$$

Substitute \frac{3}{2}A for B in the equation A=-B+2.

$$A=-\frac{3}{2}A+2$$

Solve A=-\frac{3}{2}A+2 for A.

$$A=\frac{4}{5}$$

Substitute \frac{4}{5} for A in the equation B=\frac{3}{2}A.

$$B=\frac{3}{2}\times \frac{4}{5}$$

Calculate B from B=\frac{3}{2}\times \frac{4}{5}.

$$B=\frac{6}{5}$$

Substitute \frac{4}{5} for A in the equation C=2A.

$$C=2\times \frac{4}{5}$$

Calculate C from C=2\times \frac{4}{5}.

$$C=\frac{8}{5}$$

The system is now solved.

$$A=\frac{4}{5} B=\frac{6}{5} C=\frac{8}{5}$$