\left\{ \begin{array} { l } { A + 2 B + 2 C = 2 } \\ { - 3 B + C = 3 } \\ { - A + B - C = 1 } \end{array} \right.
Solve for A, B, C
A=-4
B=0
C=3
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A=2-2B-2C
Solve A+2B+2C=2 for A.
-\left(2-2B-2C\right)+B-C=1
Substitute 2-2B-2C for A in the equation -A+B-C=1.
B=-1+\frac{1}{3}C C=3-3B
Solve the second equation for B and the third equation for C.
C=3-3\left(-1+\frac{1}{3}C\right)
Substitute -1+\frac{1}{3}C for B in the equation C=3-3B.
C=3
Solve C=3-3\left(-1+\frac{1}{3}C\right) for C.
B=-1+\frac{1}{3}\times 3
Substitute 3 for C in the equation B=-1+\frac{1}{3}C.
B=0
Calculate B from B=-1+\frac{1}{3}\times 3.
A=2-2\times 0-2\times 3
Substitute 0 for B and 3 for C in the equation A=2-2B-2C.
A=-4
Calculate A from A=2-2\times 0-2\times 3.
A=-4 B=0 C=3
The system is now solved.
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