\left\{ \begin{array} { l } { A + B = 0 } \\ { A - 2 C = 0 } \\ { B + 4 C = 0 } \end{array} \right.
Solve for A, B, C
A=0
B=0
C=0
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A=-B
Solve A+B=0 for A.
-B-2C=0
Substitute -B for A in the equation A-2C=0.
B=-2C C=-\frac{1}{4}B
Solve the second equation for B and the third equation for C.
C=-\frac{1}{4}\left(-2\right)C
Substitute -2C for B in the equation C=-\frac{1}{4}B.
C=0
Solve C=-\frac{1}{4}\left(-2\right)C for C.
B=-2\times 0
Substitute 0 for C in the equation B=-2C.
B=0
Calculate B from B=-2\times 0.
A=-0
Substitute 0 for B in the equation A=-B.
A=0
Calculate A from A=-0.
A=0 B=0 C=0
The system is now solved.
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