Examples

$4 x + 7 y = 5$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $4 x$ from both sides of the equation.

$7 y = 5 - 4 x$

Step 1.2

Divide each term in $7 y = 5 - 4 x$ by $7$ and simplify.

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Step 1.2.1

Divide each term in $7 y = 5 - 4 x$ by $7$ .

$\frac{7 y}{7} = \frac{5}{7} + \frac{- 4 x}{7}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $7$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{7 y}{7} = \frac{5}{7} + \frac{- 4 x}{7}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{5}{7} + \frac{- 4 x}{7}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

$y = \frac{5}{7} - \frac{4 x}{7}$

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.

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Step 3.1

Remove parentheses.

$y = \frac{5}{7} - \frac{4 (0)}{7}$

Step 3.2

Simplify $\frac{5}{7} - \frac{4 (0)}{7}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{5 - 4 \cdot 0}{7}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $- 4$ by $0$ .

$y = \frac{5 + 0}{7}$

Step 3.2.2.2

Add $5$ and $0$ .

$y = \frac{5}{7}$

Step 3.3

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

$(0, \frac{5}{7})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = \frac{5}{7} - \frac{4 (1)}{7}$

Step 4.2

Simplify $\frac{5}{7} - \frac{4 (1)}{7}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{5 - 4 \cdot 1}{7}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply $- 4$ by $1$ .

$y = \frac{5 - 4}{7}$

Step 4.2.2.2

Subtract $4$ from $5$ .

$y = \frac{1}{7}$

Step 4.3

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

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

Step 5

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

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Step 5.1

Remove parentheses.

$y = \frac{5}{7} - \frac{4 (2)}{7}$

Step 5.2

Simplify $\frac{5}{7} - \frac{4 (2)}{7}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{5 - 4 \cdot 2}{7}$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply $- 4$ by $2$ .

$y = \frac{5 - 8}{7}$

Step 5.2.2.2

Subtract $8$ from $5$ .

$y = \frac{- 3}{7}$

Step 5.2.2.3

Move the negative in front of the fraction.

$y = - \frac{3}{7}$

Step 5.3

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

$(2, - \frac{3}{7})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{5}{7}), (1, \frac{1}{7}), (2, - \frac{3}{7})$

Step 7

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