Finite Math Examples

$3 x - 2 y = 0$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $3 x$ from both sides of the equation.

$- 2 y = - 3 x$

Step 1.2

Divide each term in $- 2 y = - 3 x$ by $- 2$ and simplify.

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Step 1.2.1

Divide each term in $- 2 y = - 3 x$ by $- 2$ .

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 2$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.1.2

Divide $y$ by $1$ .

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

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Dividing two negative values results in a positive value.

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

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.

$y = \frac{3 (0)}{2}$

Step 3.2

Simplify $\frac{3 (0)}{2}$ .

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Step 3.2.1

Cancel the common factor of $0$ and $2$ .

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Step 3.2.1.1

Factor $2$ out of $3 (0)$ .

$y = \frac{2 (3 \cdot (0))}{2}$

Step 3.2.1.2

Cancel the common factors.

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Step 3.2.1.2.1

Factor $2$ out of $2$ .

$y = \frac{2 (3 \cdot (0))}{2 (1)}$

Step 3.2.1.2.2

Cancel the common factor.

$y = \frac{2 (3 \cdot (0))}{2 \cdot 1}$

Step 3.2.1.2.3

Rewrite the expression.

$y = \frac{3 \cdot (0)}{1}$

Step 3.2.1.2.4

Divide $3 \cdot (0)$ by $1$ .

$y = 3 \cdot (0)$

Step 3.2.2

Multiply $3$ by $0$ .

$y = 0$

Step 3.3

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

$(0, 0)$

Step 4

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

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Step 4.1

Remove parentheses.

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

Step 4.2

Multiply $3$ by $1$ .

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

Step 4.3

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

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

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

Cancel the common factor of $2$ .

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Step 5.2.1

Cancel the common factor.

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

Step 5.2.2

Divide $3$ by $1$ .

$y = 3$

Step 5.3

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

$(2, 3)$

Step 6

These are three possible solutions to the equation.

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

Step 7