Solve {l}{A+B=10}{A-B=5}{A*B=C}

$$\left. \begin{array} { l } { A + B = 10 } \\ { A - B = 5 } \\ { A \times B = C } \end{array} \right.$$

Solve for A, B, C

$$A = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

$$B = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$C = \frac{75}{4} = 18\frac{3}{4} = 18.75$$

Short Steps Using Substitution

Solve A+B=10 for A.

$$A=-B+10$$

Substitute -B+10 for A in the second and third equation.

$$-B+10-B=5 \left(-B+10\right)B=C$$

Solve these equations for B and C respectively.

$$B=\frac{5}{2} C=-B^{2}+10B$$

Substitute \frac{5}{2} for B in the equation C=-B^{2}+10B.

$$C=-\left(\frac{5}{2}\right)^{2}+10\times \frac{5}{2}$$

Calculate C from C=-\left(\frac{5}{2}\right)^{2}+10\times \frac{5}{2}.

$$C=\frac{75}{4}$$

Substitute \frac{5}{2} for B in the equation A=-B+10.

$$A=-\frac{5}{2}+10$$

Calculate A from A=-\frac{5}{2}+10.

$$A=\frac{15}{2}$$

The system is now solved.

$$A=\frac{15}{2} B=\frac{5}{2} C=\frac{75}{4}$$