Algebra Examples

$2 x - 4 y - 2 z = 0$ $0 x + 1 y + 4 z = 0$ $3 x - 6 y - 3 z = 0$

Step 1

Subtract $4 z$ from both sides of the equation.

$y = - 4 z$

$2 x - 4 y - 2 z = 0$

$3 x - 6 y - 3 z = 0$

Step 2

Replace all occurrences of $y$ with $- 4 z$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $2 x - 4 y - 2 z = 0$ with $- 4 z$ .

$2 x - 4 (- 4 z) - 2 z = 0$

$y = - 4 z$

$3 x - 6 y - 3 z = 0$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 x - 4 (- 4 z) - 2 z$ .

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Step 2.2.1.1

Multiply $- 4$ by $- 4$ .

$2 x + 16 z - 2 z = 0$

$y = - 4 z$

$3 x - 6 y - 3 z = 0$

Step 2.2.1.2

Subtract $2 z$ from $16 z$ .

$2 x + 14 z = 0$

$y = - 4 z$

$3 x - 6 y - 3 z = 0$

$2 x + 14 z = 0$

$y = - 4 z$

$3 x - 6 y - 3 z = 0$

$2 x + 14 z = 0$

$y = - 4 z$

$3 x - 6 y - 3 z = 0$

Step 2.3

Replace all occurrences of $y$ in $3 x - 6 y - 3 z = 0$ with $- 4 z$ .

$3 x - 6 (- 4 z) - 3 z = 0$

$2 x + 14 z = 0$

$y = - 4 z$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $3 x - 6 (- 4 z) - 3 z$ .

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Step 2.4.1.1

Multiply $- 4$ by $- 6$ .

$3 x + 24 z - 3 z = 0$

$2 x + 14 z = 0$

$y = - 4 z$

Step 2.4.1.2

Subtract $3 z$ from $24 z$ .

$3 x + 21 z = 0$

$2 x + 14 z = 0$

$y = - 4 z$

$3 x + 21 z = 0$

$2 x + 14 z = 0$

$y = - 4 z$

$3 x + 21 z = 0$

$2 x + 14 z = 0$

$y = - 4 z$

$3 x + 21 z = 0$

$2 x + 14 z = 0$

$y = - 4 z$

Step 3

Solve for $x$ in $3 x + 21 z = 0$ .

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Step 3.1

Subtract $21 z$ from both sides of the equation.

$3 x = - 21 z$

$2 x + 14 z = 0$

$y = - 4 z$

Step 3.2

Divide each term in $3 x = - 21 z$ by $3$ and simplify.

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Step 3.2.1

Divide each term in $3 x = - 21 z$ by $3$ .

$\frac{3 x}{3} = \frac{- 21 z}{3}$

$2 x + 14 z = 0$

$y = - 4 z$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 21 z}{3}$

$2 x + 14 z = 0$

$y = - 4 z$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 21 z}{3}$

$2 x + 14 z = 0$

$y = - 4 z$

$x = \frac{- 21 z}{3}$

$2 x + 14 z = 0$

$y = - 4 z$

$x = \frac{- 21 z}{3}$

$2 x + 14 z = 0$

$y = - 4 z$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Cancel the common factor of $- 21$ and $3$ .

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Step 3.2.3.1.1

Factor $3$ out of $- 21 z$ .

$x = \frac{3 (- 7 z)}{3}$

$2 x + 14 z = 0$

$y = - 4 z$

Step 3.2.3.1.2

Cancel the common factors.

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Step 3.2.3.1.2.1

Factor $3$ out of $3$ .

$x = \frac{3 (- 7 z)}{3 (1)}$

$2 x + 14 z = 0$

$y = - 4 z$

Step 3.2.3.1.2.2

Cancel the common factor.

$x = \frac{3 (- 7 z)}{3 \cdot 1}$

$2 x + 14 z = 0$

$y = - 4 z$

Step 3.2.3.1.2.3

Rewrite the expression.

$x = \frac{- 7 z}{1}$

$2 x + 14 z = 0$

$y = - 4 z$

Step 3.2.3.1.2.4

Divide $- 7 z$ by $1$ .

$x = - 7 z$

$2 x + 14 z = 0$

$y = - 4 z$

$x = - 7 z$

$2 x + 14 z = 0$

$y = - 4 z$

$x = - 7 z$

$2 x + 14 z = 0$

$y = - 4 z$

$x = - 7 z$

$2 x + 14 z = 0$

$y = - 4 z$

$x = - 7 z$

$2 x + 14 z = 0$

$y = - 4 z$

$x = - 7 z$

$2 x + 14 z = 0$

$y = - 4 z$

Step 4

Replace all occurrences of $x$ with $- 7 z$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $2 x + 14 z = 0$ with $- 7 z$ .

$2 (- 7 z) + 14 z = 0$

$x = - 7 z$

$y = - 4 z$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $2 (- 7 z) + 14 z$ .

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Step 4.2.1.1

Multiply $- 7$ by $2$ .

$- 14 z + 14 z = 0$

$x = - 7 z$

$y = - 4 z$

Step 4.2.1.2

Add $- 14 z$ and $14 z$ .

$0 = 0$

$x = - 7 z$

$y = - 4 z$

$0 = 0$

$x = - 7 z$

$y = - 4 z$

$0 = 0$

$x = - 7 z$

$y = - 4 z$

$0 = 0$

$x = - 7 z$

$y = - 4 z$

Step 5

Remove any equations from the system that are always true.

$x = - 7 z$

$y = - 4 z$