Finite Math Examples

$2 x - 3 y = 10$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $2 x$ from both sides of the equation.

$- 3 y = 10 - 2 x$

Step 1.2

Divide each term in $- 3 y = 10 - 2 x$ by $- 3$ and simplify.

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Step 1.2.1

Divide each term in $- 3 y = 10 - 2 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{10}{- 3} + \frac{- 2 x}{- 3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{10}{- 3} + \frac{- 2 x}{- 3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{10}{- 3} + \frac{- 2 x}{- 3}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Move the negative in front of the fraction.

$y = - \frac{10}{3} + \frac{- 2 x}{- 3}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{10}{3} + \frac{2 x}{3}$

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.

$y = - \frac{10}{3} + \frac{2 (0)}{3}$

Step 3.2

Simplify $- \frac{10}{3} + \frac{2 (0)}{3}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{- 10 + 2 (0)}{3}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $2$ by $0$ .

$y = \frac{- 10 + 0}{3}$

Step 3.2.2.2

Add $- 10$ and $0$ .

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

Step 3.2.2.3

Move the negative in front of the fraction.

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

Step 3.3

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

$(0, - \frac{10}{3})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = - \frac{10}{3} + \frac{2 (1)}{3}$

Step 4.2

Simplify $- \frac{10}{3} + \frac{2 (1)}{3}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{- 10 + 2 (1)}{3}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply $2$ by $1$ .

$y = \frac{- 10 + 2}{3}$

Step 4.2.2.2

Add $- 10$ and $2$ .

$y = \frac{- 8}{3}$

Step 4.2.2.3

Move the negative in front of the fraction.

$y = - \frac{8}{3}$

Step 4.3

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

$(1, - \frac{8}{3})$

Step 5

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

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Step 5.1

Remove parentheses.

$y = - \frac{10}{3} + \frac{2 (2)}{3}$

Step 5.2

Simplify $- \frac{10}{3} + \frac{2 (2)}{3}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{- 10 + 2 (2)}{3}$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply $2$ by $2$ .

$y = \frac{- 10 + 4}{3}$

Step 5.2.2.2

Add $- 10$ and $4$ .

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

Step 5.2.2.3

Divide $- 6$ by $3$ .

$y = - 2$

Step 5.3

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

$(2, - 2)$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{10}{3}), (1, - \frac{8}{3}), (2, - 2)$

Step 7