Algebra Examples

$A + C = 1$ $B + D = 0$ $4 A + 2 C = 0$ $4 B + 2 D = 6$

Step 1

Subtract $C$ from both sides of the equation.

$A = 1 - C$

$B + D = 0$

$4 A + 2 C = 0$

$4 B + 2 D = 6$

Step 2

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

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Step 2.1

Replace all occurrences of $A$ in $4 A + 2 C = 0$ with $1 - C$ .

$4 (1 - C) + 2 C = 0$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $4 (1 - C) + 2 C$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$4 \cdot 1 + 4 (- C) + 2 C = 0$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

Step 2.2.1.1.2

Multiply $4$ by $1$ .

$4 + 4 (- C) + 2 C = 0$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

Step 2.2.1.1.3

Multiply $- 1$ by $4$ .

$4 - 4 C + 2 C = 0$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

$4 - 4 C + 2 C = 0$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

Step 2.2.1.2

Add $- 4 C$ and $2 C$ .

$4 - 2 C = 0$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

$4 - 2 C = 0$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

$4 - 2 C = 0$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

$4 - 2 C = 0$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

Step 3

Solve for $C$ in $4 - 2 C = 0$ .

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Step 3.1

Subtract $4$ from both sides of the equation.

$- 2 C = - 4$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

Step 3.2

Divide each term in $- 2 C = - 4$ by $- 2$ and simplify.

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Step 3.2.1

Divide each term in $- 2 C = - 4$ by $- 2$ .

$\frac{- 2 C}{- 2} = \frac{- 4}{- 2}$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 2 C}{- 2} = \frac{- 4}{- 2}$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

Step 3.2.2.1.2

Divide $C$ by $1$ .

$C = \frac{- 4}{- 2}$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

$C = \frac{- 4}{- 2}$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

$C = \frac{- 4}{- 2}$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 4$ by $- 2$ .

$C = 2$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

$C = 2$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

$C = 2$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

$C = 2$

$A = 1 - C$

$B + D = 0$

$4 B + 2 D = 6$

Step 4

Replace all occurrences of $C$ with $2$ in each equation.

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Step 4.1

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

$A = 1 - (2)$

$C = 2$

$B + D = 0$

$4 B + 2 D = 6$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $1 - (2)$ .

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Step 4.2.1.1

Multiply $- 1$ by $2$ .

$A = 1 - 2$

$C = 2$

$B + D = 0$

$4 B + 2 D = 6$

Step 4.2.1.2

Subtract $2$ from $1$ .

$A = - 1$

$C = 2$

$B + D = 0$

$4 B + 2 D = 6$

$A = - 1$

$C = 2$

$B + D = 0$

$4 B + 2 D = 6$

$A = - 1$

$C = 2$

$B + D = 0$

$4 B + 2 D = 6$

$A = - 1$

$C = 2$

$B + D = 0$

$4 B + 2 D = 6$

Step 5

Subtract $D$ from both sides of the equation.

$B = - D$

$A = - 1$

$C = 2$

$4 B + 2 D = 6$

Step 6

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

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Step 6.1

Replace all occurrences of $B$ in $4 B + 2 D = 6$ with $- D$ .

$4 (- D) + 2 D = 6$

$B = - D$

$A = - 1$

$C = 2$

Step 6.2

Simplify the left side.

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Step 6.2.1

Simplify $4 (- D) + 2 D$ .

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Step 6.2.1.1

Multiply $- 1$ by $4$ .

$- 4 D + 2 D = 6$

$B = - D$

$A = - 1$

$C = 2$

Step 6.2.1.2

Add $- 4 D$ and $2 D$ .

$- 2 D = 6$

$B = - D$

$A = - 1$

$C = 2$

$- 2 D = 6$

$B = - D$

$A = - 1$

$C = 2$

$- 2 D = 6$

$B = - D$

$A = - 1$

$C = 2$

$- 2 D = 6$

$B = - D$

$A = - 1$

$C = 2$

Step 7

Divide each term in $- 2 D = 6$ by $- 2$ and simplify.

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Step 7.1

Divide each term in $- 2 D = 6$ by $- 2$ .

$\frac{- 2 D}{- 2} = \frac{6}{- 2}$

$B = - D$

$A = - 1$

$C = 2$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $- 2$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{- 2 D}{- 2} = \frac{6}{- 2}$

$B = - D$

$A = - 1$

$C = 2$

Step 7.2.1.2

Divide $D$ by $1$ .

$D = \frac{6}{- 2}$

$B = - D$

$A = - 1$

$C = 2$

$D = \frac{6}{- 2}$

$B = - D$

$A = - 1$

$C = 2$

$D = \frac{6}{- 2}$

$B = - D$

$A = - 1$

$C = 2$

Step 7.3

Simplify the right side.

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Step 7.3.1

Divide $6$ by $- 2$ .

$D = - 3$

$B = - D$

$A = - 1$

$C = 2$

$D = - 3$

$B = - D$

$A = - 1$

$C = 2$

$D = - 3$

$B = - D$

$A = - 1$

$C = 2$

Step 8

Replace all occurrences of $D$ with $- 3$ in each equation.

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Step 8.1

Replace all occurrences of $D$ in $B = - D$ with $- 3$ .

$B = - (- 3)$

$D = - 3$

$A = - 1$

$C = 2$

Step 8.2

Simplify the right side.

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Step 8.2.1

Multiply $- 1$ by $- 3$ .

$B = 3$

$D = - 3$

$A = - 1$

$C = 2$

$B = 3$

$D = - 3$

$A = - 1$

$C = 2$

$B = 3$

$D = - 3$

$A = - 1$

$C = 2$

Step 9

List all of the solutions.

$B = 3, D = - 3, A = - 1, C = 2$