Algebra Examples

$A + C = 0$ $- 3 A + B - 2 C = 0$ $2 A - 2 B + C = 1$

Step 1

Subtract $C$ from both sides of the equation.

$A = - C$

$- 3 A + B - 2 C = 0$

$2 A - 2 B + C = 1$

Step 2

Replace all occurrences of $A$ with $- C$ in each equation.

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Step 2.1

Replace all occurrences of $A$ in $- 3 A + B - 2 C = 0$ with $- C$ .

$- 3 (- C) + B - 2 C = 0$

$A = - C$

$2 A - 2 B + C = 1$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 3 (- C) + B - 2 C$ .

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Step 2.2.1.1

Multiply $- 1$ by $- 3$ .

$3 C + B - 2 C = 0$

$A = - C$

$2 A - 2 B + C = 1$

Step 2.2.1.2

Subtract $2 C$ from $3 C$ .

$B + C = 0$

$A = - C$

$2 A - 2 B + C = 1$

$B + C = 0$

$A = - C$

$2 A - 2 B + C = 1$

$B + C = 0$

$A = - C$

$2 A - 2 B + C = 1$

Step 2.3

Replace all occurrences of $A$ in $2 A - 2 B + C = 1$ with $- C$ .

$2 (- C) - 2 B + C = 1$

$B + C = 0$

$A = - C$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $2 (- C) - 2 B + C$ .

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Step 2.4.1.1

Multiply $- 1$ by $2$ .

$- 2 C - 2 B + C = 1$

$B + C = 0$

$A = - C$

Step 2.4.1.2

Add $- 2 C$ and $C$ .

$- 2 B - C = 1$

$B + C = 0$

$A = - C$

$- 2 B - C = 1$

$B + C = 0$

$A = - C$

$- 2 B - C = 1$

$B + C = 0$

$A = - C$

$- 2 B - C = 1$

$B + C = 0$

$A = - C$

Step 3

Subtract $C$ from both sides of the equation.

$B = - C$

$- 2 B - C = 1$

$A = - C$

Step 4

Replace all occurrences of $B$ with $- C$ in each equation.

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Step 4.1

Replace all occurrences of $B$ in $- 2 B - C = 1$ with $- C$ .

$- 2 (- C) - C = 1$

$B = - C$

$A = - C$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $- 2 (- C) - C$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 2$ .

$2 C - C = 1$

$B = - C$

$A = - C$

Step 4.2.1.2

Subtract $C$ from $2 C$ .

$C = 1$

$B = - C$

$A = - C$

$C = 1$

$B = - C$

$A = - C$

$C = 1$

$B = - C$

$A = - C$

$C = 1$

$B = - C$

$A = - C$

Step 5

Replace all occurrences of $C$ with $1$ in each equation.

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Step 5.1

Replace all occurrences of $C$ in $B = - C$ with $1$ .

$B = - (1)$

$C = 1$

$A = - C$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 1$ by $1$ .

$B = - 1$

$C = 1$

$A = - C$

$B = - 1$

$C = 1$

$A = - C$

Step 5.3

Replace all occurrences of $C$ in $A = - C$ with $1$ .

$A = - (1)$

$B = - 1$

$C = 1$

Step 5.4

Simplify the right side.

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Step 5.4.1

Multiply $- 1$ by $1$ .

$A = - 1$

$B = - 1$

$C = 1$

$A = - 1$

$B = - 1$

$C = 1$

$A = - 1$

$B = - 1$

$C = 1$

Step 6

List all of the solutions.

$A = - 1, B = - 1, C = 1$