Solve {l}{A+B+C=7}{A-C=4}{B-A=3}

$$\left. \begin{array} { l } { A + B + C = 7 } \\ { A - C = 4 } \\ { B - A = 3 } \end{array} \right.$$

Solve for A, B, C

$$A = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

$$B = \frac{17}{3} = 5\frac{2}{3} \approx 5.666666667$$

$$C = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

Short Steps Using Substitution

Solve A+B+C=7 for A.

$$A=-B-C+7$$

Substitute -B-C+7 for A in the second and third equation.

$$-B-C+7-C=4 B-\left(-B-C+7\right)=3$$

Solve these equations for B and C respectively.

$$B=-2C+3 C=-2B+10$$

Substitute -2C+3 for B in the equation C=-2B+10.

$$C=-2\left(-2C+3\right)+10$$

Solve C=-2\left(-2C+3\right)+10 for C.

$$C=-\frac{4}{3}$$

Substitute -\frac{4}{3} for C in the equation B=-2C+3.

$$B=-2\left(-\frac{4}{3}\right)+3$$

Calculate B from B=-2\left(-\frac{4}{3}\right)+3.

$$B=\frac{17}{3}$$

Substitute \frac{17}{3} for B and -\frac{4}{3} for C in the equation A=-B-C+7.

$$A=-\frac{17}{3}-\left(-\frac{4}{3}\right)+7$$

Calculate A from A=-\frac{17}{3}-\left(-\frac{4}{3}\right)+7.

$$A=\frac{8}{3}$$

The system is now solved.

$$A=\frac{8}{3} B=\frac{17}{3} C=-\frac{4}{3}$$