Algebra Examples

$2 x - 2 y + 4 z = 5$ $4 x - 4 y + 5 z = 4$ $2 z = 4$

Step 1

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

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Step 1.1

Divide each term in $2 z = 4$ by $2$ .

$\frac{2 z}{2} = \frac{4}{2}$

$2 x - 2 y + 4 z = 5$

$4 x - 4 y + 5 z = 4$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 z}{2} = \frac{4}{2}$

$2 x - 2 y + 4 z = 5$

$4 x - 4 y + 5 z = 4$

Step 1.2.1.2

Divide $z$ by $1$ .

$z = \frac{4}{2}$

$2 x - 2 y + 4 z = 5$

$4 x - 4 y + 5 z = 4$

$z = \frac{4}{2}$

$2 x - 2 y + 4 z = 5$

$4 x - 4 y + 5 z = 4$

$z = \frac{4}{2}$

$2 x - 2 y + 4 z = 5$

$4 x - 4 y + 5 z = 4$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $4$ by $2$ .

$z = 2$

$2 x - 2 y + 4 z = 5$

$4 x - 4 y + 5 z = 4$

$z = 2$

$2 x - 2 y + 4 z = 5$

$4 x - 4 y + 5 z = 4$

$z = 2$

$2 x - 2 y + 4 z = 5$

$4 x - 4 y + 5 z = 4$

Step 2

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

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Step 2.1

Replace all occurrences of $z$ in $2 x - 2 y + 4 z = 5$ with $2$ .

$2 x - 2 y + 4 (2) = 5$

$z = 2$

$4 x - 4 y + 5 z = 4$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $4$ by $2$ .

$2 x - 2 y + 8 = 5$

$z = 2$

$4 x - 4 y + 5 z = 4$

$2 x - 2 y + 8 = 5$

$z = 2$

$4 x - 4 y + 5 z = 4$

Step 2.3

Replace all occurrences of $z$ in $4 x - 4 y + 5 z = 4$ with $2$ .

$4 x - 4 y + 5 (2) = 4$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 2.4

Simplify the left side.

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Step 2.4.1

Multiply $5$ by $2$ .

$4 x - 4 y + 10 = 4$

$2 x - 2 y + 8 = 5$

$z = 2$

$4 x - 4 y + 10 = 4$

$2 x - 2 y + 8 = 5$

$z = 2$

$4 x - 4 y + 10 = 4$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3

Solve for $x$ in $4 x - 4 y + 10 = 4$ .

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Step 3.1

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1.1

Add $4 y$ to both sides of the equation.

$4 x + 10 = 4 + 4 y$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3.1.2

Subtract $10$ from both sides of the equation.

$4 x = 4 + 4 y - 10$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3.1.3

Subtract $10$ from $4$ .

$4 x = 4 y - 6$

$2 x - 2 y + 8 = 5$

$z = 2$

$4 x = 4 y - 6$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3.2

Divide each term in $4 x = 4 y - 6$ by $4$ and simplify.

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Step 3.2.1

Divide each term in $4 x = 4 y - 6$ by $4$ .

$\frac{4 x}{4} = \frac{4 y}{4} + \frac{- 6}{4}$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{4 y}{4} + \frac{- 6}{4}$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{4 y}{4} + \frac{- 6}{4}$

$2 x - 2 y + 8 = 5$

$z = 2$

$x = \frac{4 y}{4} + \frac{- 6}{4}$

$2 x - 2 y + 8 = 5$

$z = 2$

$x = \frac{4 y}{4} + \frac{- 6}{4}$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Cancel the common factor of $4$ .

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Step 3.2.3.1.1.1

Cancel the common factor.

$x = \frac{4 y}{4} + \frac{- 6}{4}$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3.2.3.1.1.2

Divide $y$ by $1$ .

$x = y + \frac{- 6}{4}$

$2 x - 2 y + 8 = 5$

$z = 2$

$x = y + \frac{- 6}{4}$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3.2.3.1.2

Cancel the common factor of $- 6$ and $4$ .

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Step 3.2.3.1.2.1

Factor $2$ out of $- 6$ .

$x = y + \frac{2 (- 3)}{4}$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3.2.3.1.2.2

Cancel the common factors.

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Step 3.2.3.1.2.2.1

Factor $2$ out of $4$ .

$x = y + \frac{2 \cdot - 3}{2 \cdot 2}$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3.2.3.1.2.2.2

Cancel the common factor.

$x = y + \frac{2 \cdot - 3}{2 \cdot 2}$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3.2.3.1.2.2.3

Rewrite the expression.

$x = y + \frac{- 3}{2}$

$2 x - 2 y + 8 = 5$

$z = 2$

$x = y + \frac{- 3}{2}$

$2 x - 2 y + 8 = 5$

$z = 2$

$x = y + \frac{- 3}{2}$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 3.2.3.1.3

Move the negative in front of the fraction.

$x = y - \frac{3}{2}$

$2 x - 2 y + 8 = 5$

$z = 2$

$x = y - \frac{3}{2}$

$2 x - 2 y + 8 = 5$

$z = 2$

$x = y - \frac{3}{2}$

$2 x - 2 y + 8 = 5$

$z = 2$

$x = y - \frac{3}{2}$

$2 x - 2 y + 8 = 5$

$z = 2$

$x = y - \frac{3}{2}$

$2 x - 2 y + 8 = 5$

$z = 2$

Step 4

Replace all occurrences of $x$ with $y - \frac{3}{2}$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $2 x - 2 y + 8 = 5$ with $y - \frac{3}{2}$ .

$2 (y - \frac{3}{2}) - 2 y + 8 = 5$

$x = y - \frac{3}{2}$

$z = 2$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $2 (y - \frac{3}{2}) - 2 y + 8$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Apply the distributive property.

$2 y + 2 (- \frac{3}{2}) - 2 y + 8 = 5$

$x = y - \frac{3}{2}$

$z = 2$

Step 4.2.1.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.1.2.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$2 y + 2 (\frac{- 3}{2}) - 2 y + 8 = 5$

$x = y - \frac{3}{2}$

$z = 2$

Step 4.2.1.1.2.2

Cancel the common factor.

$2 y + 2 (\frac{- 3}{2}) - 2 y + 8 = 5$

$x = y - \frac{3}{2}$

$z = 2$

Step 4.2.1.1.2.3

Rewrite the expression.

$2 y - 3 - 2 y + 8 = 5$

$x = y - \frac{3}{2}$

$z = 2$

$2 y - 3 - 2 y + 8 = 5$

$x = y - \frac{3}{2}$

$z = 2$

$2 y - 3 - 2 y + 8 = 5$

$x = y - \frac{3}{2}$

$z = 2$

Step 4.2.1.2

Simplify by adding terms.

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Step 4.2.1.2.1

Combine the opposite terms in $2 y - 3 - 2 y + 8$ .

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Step 4.2.1.2.1.1

Subtract $2 y$ from $2 y$ .

$0 - 3 + 8 = 5$

$x = y - \frac{3}{2}$

$z = 2$

Step 4.2.1.2.1.2

Subtract $3$ from $0$ .

$- 3 + 8 = 5$

$x = y - \frac{3}{2}$

$z = 2$

$- 3 + 8 = 5$

$x = y - \frac{3}{2}$

$z = 2$

Step 4.2.1.2.2

Add $- 3$ and $8$ .

$5 = 5$

$x = y - \frac{3}{2}$

$z = 2$

$5 = 5$

$x = y - \frac{3}{2}$

$z = 2$

$5 = 5$

$x = y - \frac{3}{2}$

$z = 2$

$5 = 5$

$x = y - \frac{3}{2}$

$z = 2$

$5 = 5$

$x = y - \frac{3}{2}$

$z = 2$

Step 5

Remove any equations from the system that are always true.

$x = y - \frac{3}{2}$

$z = 2$