Find Three Ordered Pair Solutions 2x+7y=11

$2 x + 7 y = 11$

Step 1

Solve the equation for $y$ .

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

$7 y = 11 - 2 x$

Divide each term in $7 y = 11 - 2 x$ by $7$ and simplify.

Divide each term in $7 y = 11 - 2 x$ by $7$ .

$\frac{7 y}{7} = \frac{11}{7} + \frac{- 2 x}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{11}{7} + \frac{- 2 x}{7}$

Divide $y$ by $1$ .

$y = \frac{11}{7} + \frac{- 2 x}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{11}{7} - \frac{2 x}{7}$

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.

$y = \frac{11}{7} - \frac{2 (0)}{7}$

Simplify $\frac{11}{7} - \frac{2 (0)}{7}$ .

Combine the numerators over the common denominator.

$y = \frac{11 - 2 \cdot 0}{7}$

Simplify the expression.

Multiply $- 2$ by $0$ .

$y = \frac{11 + 0}{7}$

Add $11$ and $0$ .

$y = \frac{11}{7}$

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

$(0, \frac{11}{7})$

Step 4

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

Remove parentheses.

$y = \frac{11}{7} - \frac{2 (1)}{7}$

Simplify $\frac{11}{7} - \frac{2 (1)}{7}$ .

Combine the numerators over the common denominator.

$y = \frac{11 - 2 \cdot 1}{7}$

Simplify the expression.

Multiply $- 2$ by $1$ .

$y = \frac{11 - 2}{7}$

Subtract $2$ from $11$ .

$y = \frac{9}{7}$

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

$(1, \frac{9}{7})$

Step 5

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

Remove parentheses.

$y = \frac{11}{7} - \frac{2 (2)}{7}$

Simplify $\frac{11}{7} - \frac{2 (2)}{7}$ .

Combine the numerators over the common denominator.

$y = \frac{11 - 2 \cdot 2}{7}$

Simplify the expression.

Multiply $- 2$ by $2$ .

$y = \frac{11 - 4}{7}$

Subtract $4$ from $11$ .

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

Divide $7$ by $7$ .

$y = 1$

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

$(2, 1)$

Step 6

These are three possible solutions to the equation.

$(0, \frac{11}{7}), (1, \frac{9}{7}), (2, 1)$

Step 7

Find Three Ordered Pair Solutions 2x+7y=11

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