Finite Math Examples

$3 y = 7 - 3 x$

Step 1

Divide each term in $3 y = 7 - 3 x$ by $3$ and simplify.

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Step 1.1

Divide each term in $3 y = 7 - 3 x$ by $3$ .

$\frac{3 y}{3} = \frac{7}{3} + \frac{- 3 x}{3}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $3$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{7}{3} + \frac{- 3 x}{3}$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{7}{3} + \frac{- 3 x}{3}$

Step 1.3

Simplify the right side.

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Step 1.3.1

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

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Step 1.3.1.1

Factor $3$ out of $- 3 x$ .

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

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $3$ out of $3$ .

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

Step 1.3.1.2.2

Cancel the common factor.

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

Step 1.3.1.2.3

Rewrite the expression.

$y = \frac{7}{3} + \frac{- x}{1}$

Step 1.3.1.2.4

Divide $- x$ by $1$ .

$y = \frac{7}{3} - x$

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.

$y = \frac{7}{3} - (0)$

Step 3.2

Subtract $0$ from $\frac{7}{3}$ .

$y = \frac{7}{3}$

Step 3.3

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

$(0, \frac{7}{3})$

Step 4

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

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Step 4.1

Remove parentheses.

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

Step 4.2

Simplify $\frac{7}{3} - (1)$ .

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Step 4.2.1

Multiply $- 1$ by $1$ .

$y = \frac{7}{3} - 1$

Step 4.2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{7}{3} - 1 \cdot \frac{3}{3}$

Step 4.2.3

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

$y = \frac{7}{3} + \frac{- 1 \cdot 3}{3}$

Step 4.2.4

Combine the numerators over the common denominator.

$y = \frac{7 - 1 \cdot 3}{3}$

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $- 1$ by $3$ .

$y = \frac{7 - 3}{3}$

Step 4.2.5.2

Subtract $3$ from $7$ .

$y = \frac{4}{3}$

Step 4.3

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

$(1, \frac{4}{3})$

Step 5

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

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Step 5.1

Remove parentheses.

$y = \frac{7}{3} - (2)$

Step 5.2

Simplify $\frac{7}{3} - (2)$ .

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Step 5.2.1

Multiply $- 1$ by $2$ .

$y = \frac{7}{3} - 2$

Step 5.2.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{7}{3} - 2 \cdot \frac{3}{3}$

Step 5.2.3

Combine $- 2$ and $\frac{3}{3}$ .

$y = \frac{7}{3} + \frac{- 2 \cdot 3}{3}$

Step 5.2.4

Combine the numerators over the common denominator.

$y = \frac{7 - 2 \cdot 3}{3}$

Step 5.2.5

Simplify the numerator.

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Step 5.2.5.1

Multiply $- 2$ by $3$ .

$y = \frac{7 - 6}{3}$

Step 5.2.5.2

Subtract $6$ from $7$ .

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

Step 5.3

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

$(2, \frac{1}{3})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{7}{3}), (1, \frac{4}{3}), (2, \frac{1}{3})$

Step 7