Algebra Examples

$7 x - 2 y = - 5$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $7 x$ from both sides of the equation.

$- 2 y = - 5 - 7 x$

Step 1.2

Divide each term in $- 2 y = - 5 - 7 x$ by $- 2$ and simplify.

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Step 1.2.1

Divide each term in $- 2 y = - 5 - 7 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 5}{- 2} + \frac{- 7 x}{- 2}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 5}{- 2} + \frac{- 7 x}{- 2}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 5}{- 2} + \frac{- 7 x}{- 2}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Dividing two negative values results in a positive value.

$y = \frac{5}{2} + \frac{- 7 x}{- 2}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = \frac{5}{2} + \frac{7 x}{2}$

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.

$y = \frac{5}{2} + \frac{7 (0)}{2}$

Step 3.2

Simplify $\frac{5}{2} + \frac{7 (0)}{2}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{5 + 7 (0)}{2}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $7$ by $0$ .

$y = \frac{5 + 0}{2}$

Step 3.2.2.2

Add $5$ and $0$ .

$y = \frac{5}{2}$

Step 3.3

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

$(0, \frac{5}{2})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = \frac{5}{2} + \frac{7 (1)}{2}$

Step 4.2

Simplify $\frac{5}{2} + \frac{7 (1)}{2}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{5 + 7 (1)}{2}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply $7$ by $1$ .

$y = \frac{5 + 7}{2}$

Step 4.2.2.2

Add $5$ and $7$ .

$y = \frac{12}{2}$

Step 4.2.2.3

Divide $12$ by $2$ .

$y = 6$

Step 4.3

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

$(1, 6)$

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

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

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Step 5.2.1

Combine the numerators over the common denominator.

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

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply $7$ by $2$ .

$y = \frac{5 + 14}{2}$

Step 5.2.2.2

Add $5$ and $14$ .

$y = \frac{19}{2}$

Step 5.3

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

$(2, \frac{19}{2})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{5}{2}), (1, 6), (2, \frac{19}{2})$

Step 7