Find Three Ordered Pair Solutions 3x-7y=-14

$3 x - 7 y = - 14$

Step 1

Solve the equation for $y$ .

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

$- 7 y = - 14 - 3 x$

Divide each term in $- 7 y = - 14 - 3 x$ by $- 7$ and simplify.

Divide each term in $- 7 y = - 14 - 3 x$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 14}{- 7} + \frac{- 3 x}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 14}{- 7} + \frac{- 3 x}{- 7}$

Divide $y$ by $1$ .

$y = \frac{- 14}{- 7} + \frac{- 3 x}{- 7}$

Simplify the right side.

Simplify each term.

Divide $- 14$ by $- 7$ .

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

Dividing two negative values results in a positive value.

$y = 2 + \frac{3 x}{7}$

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.

Remove parentheses.

$y = 2 + \frac{3 (0)}{7}$

Simplify $2 + \frac{3 (0)}{7}$ .

Multiply $3$ by $0$ .

$y = 2 + \frac{0}{7}$

Divide $0$ by $7$ .

$y = 2 + 0$

Add $2$ and $0$ .

$y = 2$

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

$(0, 2)$

Step 4

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

Remove parentheses.

$y = 2 + \frac{3 (1)}{7}$

Simplify $2 + \frac{3 (1)}{7}$ .

Multiply $3$ by $1$ .

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

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

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

Combine $2$ and $\frac{7}{7}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $7$ .

$y = \frac{14 + 3}{7}$

Add $14$ and $3$ .

$y = \frac{17}{7}$

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

$(1, \frac{17}{7})$

Step 5

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

Remove parentheses.

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

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

Multiply $3$ by $2$ .

$y = 2 + \frac{6}{7}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = 2 \cdot \frac{7}{7} + \frac{6}{7}$

Combine $2$ and $\frac{7}{7}$ .

$y = \frac{2 \cdot 7}{7} + \frac{6}{7}$

Combine the numerators over the common denominator.

$y = \frac{2 \cdot 7 + 6}{7}$

Simplify the numerator.

Multiply $2$ by $7$ .

$y = \frac{14 + 6}{7}$

Add $14$ and $6$ .

$y = \frac{20}{7}$

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

$(2, \frac{20}{7})$

Step 6

These are three possible solutions to the equation.

$(0, 2), (1, \frac{17}{7}), (2, \frac{20}{7})$

Step 7

Find Three Ordered Pair Solutions 3x-7y=-14

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