Solve {l}{A+B+C=0}{-B+C=0}{-A=1}

$$\left\{ \begin{array} { l } { A + B + C = 0 } \\ { - B + C = 0 } \\ { - A = 1 } \end{array} \right.$$

Solve for A, B, C

$$A=-1$$

$$B=\frac{1}{2}=0.5$$

$$C=\frac{1}{2}=0.5$$

Short Steps Using Substitution

Solve A+B+C=0 for A.

$$A=-B-C$$

Substitute -B-C for A in the equation -A=1.

$$-\left(-B-C\right)=1$$

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

$$B=C C=-B+1$$

Substitute C for B in the equation C=-B+1.

$$C=-C+1$$

Solve C=-C+1 for C.

$$C=\frac{1}{2}$$

Substitute \frac{1}{2} for C in the equation B=C.

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

Substitute \frac{1}{2} for B and \frac{1}{2} for C in the equation A=-B-C.

$$A=-\frac{1}{2}-\frac{1}{2}$$

Calculate A from A=-\frac{1}{2}-\frac{1}{2}.

$$A=-1$$

The system is now solved.

$$A=-1 B=\frac{1}{2} C=\frac{1}{2}$$