Finite Math Examples

$x + 3 y + z = 98$

Step 1

Solve the equation for $y$ .

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Step 1.1

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

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Step 1.1.1

Subtract $x$ from both sides of the equation.

$3 y + z = 98 - x$

Step 1.1.2

Subtract $z$ from both sides of the equation.

$3 y = 98 - x - z$

Step 1.2

Divide each term in $3 y = 98 - x - z$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 y = 98 - x - z$ by $3$ .

$\frac{3 y}{3} = \frac{98}{3} + \frac{- x}{3} + \frac{- z}{3}$

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.

$\frac{3 y}{3} = \frac{98}{3} + \frac{- x}{3} + \frac{- z}{3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{98}{3} + \frac{- x}{3} + \frac{- z}{3}$

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.

$y = \frac{98}{3} - \frac{x}{3} + \frac{- z}{3}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y = \frac{98}{3} - \frac{x}{3} - \frac{z}{3}$

Step 2

Choose any values for $x$ and $y$ that are in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ and $1$ to substitute for $z$ .

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Step 3.1

Remove parentheses.

$y = \frac{98}{3} - \frac{0}{3} - \frac{1}{3}$

Step 3.2

Simplify $\frac{98}{3} - \frac{0}{3} - \frac{1}{3}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{98 - 1}{3}$

Step 3.2.2

Subtract $1$ from $98$ .

$y = \frac{97}{3}$

Step 3.3

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

$(0, \frac{97}{3}, 1)$

Step 4

Choose $1$ to substitute in for $x$ and $2$ to substitute for $z$ .

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Step 4.1

Remove parentheses.

$y = \frac{98}{3} - \frac{1}{3} - \frac{2}{3}$

Step 4.2

Simplify $\frac{98}{3} - \frac{1}{3} - \frac{2}{3}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{98 - 1 - 2}{3}$

Step 4.2.2

Simplify by subtracting numbers.

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Step 4.2.2.1

Subtract $1$ from $98$ .

$y = \frac{97 - 2}{3}$

Step 4.2.2.2

Subtract $2$ from $97$ .

$y = \frac{95}{3}$

Step 4.3

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

$(1, \frac{95}{3}, 2)$

Step 5

Choose $2$ to substitute in for $x$ and $3$ to substitute for $z$ .

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Step 5.1

Remove parentheses.

$y = \frac{98}{3} - \frac{2}{3} - \frac{3}{3}$

Step 5.2

Simplify $\frac{98}{3} - \frac{2}{3} - \frac{3}{3}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{98 - 2 - 3}{3}$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Subtract $2$ from $98$ .

$y = \frac{96 - 3}{3}$

Step 5.2.2.2

Subtract $3$ from $96$ .

$y = \frac{93}{3}$

Step 5.2.2.3

Divide $93$ by $3$ .

$y = 31$

Step 5.3

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

$(2, 31, 3)$

Step 6

These are three possible solutions to the equation.

$(0, \frac{97}{3}, 1), (1, \frac{95}{3}, 2), (2, 31, 3)$