Finite Math Examples

$7 x + 9 = 6 x + 3 y$

Step 1

Solve the equation for $y$ .

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Step 1.1

Rewrite the equation as $6 x + 3 y = 7 x + 9$ .

$6 x + 3 y = 7 x + 9$

Step 1.2

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

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Step 1.2.1

Subtract $6 x$ from both sides of the equation.

$3 y = 7 x + 9 - 6 x$

Step 1.2.2

Subtract $6 x$ from $7 x$ .

$3 y = x + 9$

Step 1.3

Divide each term in $3 y = x + 9$ by $3$ and simplify.

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Step 1.3.1

Divide each term in $3 y = x + 9$ by $3$ .

$\frac{3 y}{3} = \frac{x}{3} + \frac{9}{3}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $3$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{x}{3} + \frac{9}{3}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{x}{3} + \frac{9}{3}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Divide $9$ by $3$ .

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

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 3.1

Remove parentheses.

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

Step 3.2

Simplify $\frac{0}{3} + 3$ .

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Step 3.2.1

Divide $0$ by $3$ .

$y = 0 + 3$

Step 3.2.2

Add $0$ and $3$ .

$y = 3$

Step 3.3

Use the $x$ and $y$ values to form the ordered pair.

$(0, 3)$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = \frac{1}{3} + 3$

Step 4.2

Simplify $\frac{1}{3} + 3$ .

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Step 4.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{1}{3} + 3 \cdot \frac{3}{3}$

Step 4.2.2

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

$y = \frac{1}{3} + \frac{3 \cdot 3}{3}$

Step 4.2.3

Combine the numerators over the common denominator.

$y = \frac{1 + 3 \cdot 3}{3}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $3$ by $3$ .

$y = \frac{1 + 9}{3}$

Step 4.2.4.2

Add $1$ and $9$ .

$y = \frac{10}{3}$

Step 4.3

Use the $x$ and $y$ values to form the ordered pair.

$(1, \frac{10}{3})$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

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

Step 5.2

Simplify $\frac{2}{3} + 3$ .

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Step 5.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 5.2.2

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

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

Step 5.2.3

Combine the numerators over the common denominator.

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

Step 5.2.4

Simplify the numerator.

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Step 5.2.4.1

Multiply $3$ by $3$ .

$y = \frac{2 + 9}{3}$

Step 5.2.4.2

Add $2$ and $9$ .

$y = \frac{11}{3}$

Step 5.3

Use the $x$ and $y$ values to form the ordered pair.

$(2, \frac{11}{3})$

Step 6

These are three possible solutions to the equation.

$(0, 3), (1, \frac{10}{3}), (2, \frac{11}{3})$

Step 7