Algebra Examples

$6 x - y = 9$ $\frac{1}{3} y = - 3 + 2 x$

Step 1

Solve for $x$ in $6 x - y = 9$ .

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Step 1.1

Add $y$ to both sides of the equation.

$6 x = 9 + y$

$\frac{1}{3} y = - 3 + 2 x$

Step 1.2

Divide each term in $6 x = 9 + y$ by $6$ and simplify.

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Step 1.2.1

Divide each term in $6 x = 9 + y$ by $6$ .

$\frac{6 x}{6} = \frac{9}{6} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $6$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{9}{6} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{9}{6} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

$x = \frac{9}{6} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

$x = \frac{9}{6} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Cancel the common factor of $9$ and $6$ .

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Step 1.2.3.1.1

Factor $3$ out of $9$ .

$x = \frac{3 (3)}{6} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

Step 1.2.3.1.2

Cancel the common factors.

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Step 1.2.3.1.2.1

Factor $3$ out of $6$ .

$x = \frac{3 \cdot 3}{3 \cdot 2} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

Step 1.2.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot 3}{3 \cdot 2} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

Step 1.2.3.1.2.3

Rewrite the expression.

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{1}{3} y = - 3 + 2 x$

Step 2

Replace all occurrences of $x$ with $\frac{3}{2} + \frac{y}{6}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $\frac{1}{3} y = - 3 + 2 x$ with $\frac{3}{2} + \frac{y}{6}$ .

$\frac{1}{3} y = - 3 + 2 (\frac{3}{2} + \frac{y}{6})$

$x = \frac{3}{2} + \frac{y}{6}$

Step 2.2

Simplify $\frac{1}{3} y = - 3 + 2 (\frac{3}{2} + \frac{y}{6})$ .

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Combine $\frac{1}{3}$ and $y$ .

$\frac{y}{3} = - 3 + 2 (\frac{3}{2} + \frac{y}{6})$

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{y}{3} = - 3 + 2 (\frac{3}{2} + \frac{y}{6})$

$x = \frac{3}{2} + \frac{y}{6}$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Simplify $- 3 + 2 (\frac{3}{2} + \frac{y}{6})$ .

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Step 2.2.2.1.1

Simplify each term.

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Step 2.2.2.1.1.1

Apply the distributive property.

$\frac{y}{3} = - 3 + 2 (\frac{3}{2}) + 2 (\frac{y}{6})$

$x = \frac{3}{2} + \frac{y}{6}$

Step 2.2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.2.1.1.2.1

Cancel the common factor.

$\frac{y}{3} = - 3 + 2 (\frac{3}{2}) + 2 (\frac{y}{6})$

$x = \frac{3}{2} + \frac{y}{6}$

Step 2.2.2.1.1.2.2

Rewrite the expression.

$\frac{y}{3} = - 3 + 3 + 2 (\frac{y}{6})$

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{y}{3} = - 3 + 3 + 2 (\frac{y}{6})$

$x = \frac{3}{2} + \frac{y}{6}$

Step 2.2.2.1.1.3

Cancel the common factor of $2$ .

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Step 2.2.2.1.1.3.1

Factor $2$ out of $6$ .

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

$x = \frac{3}{2} + \frac{y}{6}$

Step 2.2.2.1.1.3.2

Cancel the common factor.

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

$x = \frac{3}{2} + \frac{y}{6}$

Step 2.2.2.1.1.3.3

Rewrite the expression.

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

$x = \frac{3}{2} + \frac{y}{6}$

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

$x = \frac{3}{2} + \frac{y}{6}$

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

$x = \frac{3}{2} + \frac{y}{6}$

Step 2.2.2.1.2

Simplify by adding numbers.

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Step 2.2.2.1.2.1

Add $- 3$ and $3$ .

$\frac{y}{3} = 0 + \frac{y}{3}$

$x = \frac{3}{2} + \frac{y}{6}$

Step 2.2.2.1.2.2

Add $0$ and $\frac{y}{3}$ .

$\frac{y}{3} = \frac{y}{3}$

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{y}{3} = \frac{y}{3}$

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{y}{3} = \frac{y}{3}$

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{y}{3} = \frac{y}{3}$

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{y}{3} = \frac{y}{3}$

$x = \frac{3}{2} + \frac{y}{6}$

$\frac{y}{3} = \frac{y}{3}$

$x = \frac{3}{2} + \frac{y}{6}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{3}{2} + \frac{y}{6}$

Step 4