Find Three Ordered Pair Solutions 3x+2y=17

$3 x + 2 y = 17$

Solve the equation for $y$ .

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

$2 y = 17 - 3 x$

Divide each term by $2$ and simplify.

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Divide each term in $2 y = 17 - 3 x$ by $2$ .

$\frac{2 y}{2} = \frac{17}{2} + \frac{- 3 x}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 y}{2} = \frac{17}{2} + \frac{- 3 x}{2}$

Divide $y$ by $1$ .

$y = \frac{17}{2} + \frac{- 3 x}{2}$

Move the negative in front of the fraction.

$y = \frac{17}{2} - \frac{3 x}{2}$

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

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

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Remove parentheses.

$y = \frac{17}{2} - \frac{3 (0)}{2}$

Simplify $\frac{17}{2} - \frac{3 (0)}{2}$ .

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Simplify each term.

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

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

$y = \frac{17}{2} - \frac{2 (3 \cdot (0))}{2}$

Cancel the common factors.

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Factor $2$ out of $2$ .

$y = \frac{17}{2} - \frac{2 (3 \cdot (0))}{2 (1)}$

Cancel the common factor.

$y = \frac{17}{2} - \frac{2 (3 \cdot (0))}{2 \cdot 1}$

Rewrite the expression.

$y = \frac{17}{2} - \frac{3 \cdot (0)}{1}$

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

$y = \frac{17}{2} - (3 \cdot (0))$

Multiply $3$ by $0$ .

$y = \frac{17}{2} - 0$

Multiply $- 1$ by $0$ .

$y = \frac{17}{2} + 0$

Add $\frac{17}{2}$ and $0$ .

$y = \frac{17}{2}$

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

$(0, \frac{17}{2})$

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

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Remove parentheses.

$y = \frac{17}{2} - \frac{3 (1)}{2}$

Simplify $\frac{17}{2} - \frac{3 (1)}{2}$ .

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Multiply $3$ by $1$ .

$y = \frac{17}{2} - \frac{3}{2}$

Combine the numerators over the common denominator.

$y = \frac{17 - 3}{2}$

Subtract $3$ from $17$ .

$y = \frac{14}{2}$

Divide $14$ by $2$ .

$y = 7$

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

$(1, 7)$

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

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Remove parentheses.

$y = \frac{17}{2} - \frac{3 (2)}{2}$

Simplify $\frac{17}{2} - \frac{3 (2)}{2}$ .

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Simplify each term.

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Cancel the common factor of $2$ .

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Cancel the common factor.

$y = \frac{17}{2} - \frac{3 \cdot 2}{2}$

Divide $3$ by $1$ .

$y = \frac{17}{2} - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$y = \frac{17}{2} - 3$

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

$y = \frac{17}{2} - 3 \cdot \frac{2}{2}$

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

$y = \frac{17}{2} + \frac{- 3 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = \frac{17 - 3 \cdot 2}{2}$

Simplify the numerator.

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Multiply $- 3$ by $2$ .

$y = \frac{17 - 6}{2}$

Subtract $6$ from $17$ .

$y = \frac{11}{2}$

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

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

These are three possible solutions to the equation.

$(0, \frac{17}{2}), (1, 7), (2, \frac{11}{2})$

Find Three Ordered Pair Solutions 3x+2y=17

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