Examples

4 x + 7 y = 5

$4 x + 7 y = 5$

Step 1

Solve the equation for

y

$y$ .

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Step 1.1

Subtract

4 x

$4 x$ from both sides of the equation.

7 y = 5 - 4 x

$7 y = 5 - 4 x$

Step 1.2

Divide each term in

7 y = 5 - 4 x

$7 y = 5 - 4 x$ by

7

$7$ and simplify.

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Step 1.2.1

Divide each term in

7 y = 5 - 4 x

$7 y = 5 - 4 x$ by

7

$7$ .

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

$7$ .

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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}

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

Step 1.2.2.1.2

Divide

y

$y$ by

1

$1$ .

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

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

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

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

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

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

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}

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

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

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

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

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

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

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

Step 2

Choose any value for

x

$x$ that is in the domain to plug into the equation.

Step 3

Choose

0

$0$ to substitute in for

x

$x$ to find the ordered pair.

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Step 3.1

Remove parentheses.

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

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

Step 3.2

Simplify

\frac{5}{7} - \frac{4 (0)}{7}

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

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Step 3.2.1

Combine the numerators over the common denominator.

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

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

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply

- 4

$- 4$ by

0

$0$ .

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

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

Step 3.2.2.2

Add

5

$5$ and

0

$0$ .

y = \frac{5}{7}

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

y = \frac{5}{7}

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

y = \frac{5}{7}

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

Step 3.3

Use the

x

$x$ and

y

$y$ values to form the ordered pair.

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

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

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

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

Step 4

Choose

1

$1$ to substitute in for

x

$x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

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

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

Step 4.2

Simplify

\frac{5}{7} - \frac{4 (1)}{7}

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

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Step 4.2.1

Combine the numerators over the common denominator.

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

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

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply

- 4

$- 4$ by

1

$1$ .

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

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

Step 4.2.2.2

Subtract

4

$4$ from

5

$5$ .

y = \frac{1}{7}

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

y = \frac{1}{7}

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

y = \frac{1}{7}

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

Step 4.3

Use the

x

$x$ and

y

$y$ values to form the ordered pair.

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

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

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

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

Step 5

Choose

2

$2$ to substitute in for

x

$x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

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

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

Step 5.2

Simplify

\frac{5}{7} - \frac{4 (2)}{7}

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

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Step 5.2.1

Combine the numerators over the common denominator.

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

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

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply

- 4

$- 4$ by

2

$2$ .

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

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

Step 5.2.2.2

Subtract

8

$8$ from

5

$5$ .

y = \frac{- 3}{7}

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

Step 5.2.2.3

Move the negative in front of the fraction.

y = - \frac{3}{7}

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

y = - \frac{3}{7}

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

y = - \frac{3}{7}

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

Step 5.3

Use the

x

$x$ and

y

$y$ values to form the ordered pair.

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

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

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

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

Step 6

These are three possible solutions to the equation.

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

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

Step 7

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