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.

Simplify each term.

Dividing two negative values results in a positive value.

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

Dividing two negative values results in a positive value.

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

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.

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

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.

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

Simplify the expression.

Multiply $2$ by $1$ .

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

Add $11$ and $2$ .

$y = \frac{13}{7}$

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

$(1, \frac{13}{7})$

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.

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

Simplify the expression.

Multiply $2$ by $2$ .

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

Add $11$ and $4$ .

$y = \frac{15}{7}$

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

$(2, \frac{15}{7})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{11}{7}), (1, \frac{13}{7}), (2, \frac{15}{7})$

Step 7

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

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