Algebra Examples

$3 x + 5 y = - 17$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $3 x$ from both sides of the equation.

$5 y = - 17 - 3 x$

Step 1.2

Divide each term in $5 y = - 17 - 3 x$ by $5$ and simplify.

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Step 1.2.1

Divide each term in $5 y = - 17 - 3 x$ by $5$ .

$\frac{5 y}{5} = \frac{- 17}{5} + \frac{- 3 x}{5}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 17}{5} + \frac{- 3 x}{5}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 17}{5} + \frac{- 3 x}{5}$

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

Move the negative in front of the fraction.

$y = - \frac{17}{5} + \frac{- 3 x}{5}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{17}{5} - \frac{3 x}{5}$

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.

$y = - \frac{17}{5} - \frac{3 (0)}{5}$

Step 3.2

Simplify $- \frac{17}{5} - \frac{3 (0)}{5}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{- 17 - 3 \cdot 0}{5}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $- 3$ by $0$ .

$y = \frac{- 17 + 0}{5}$

Step 3.2.2.2

Add $- 17$ and $0$ .

$y = \frac{- 17}{5}$

Step 3.2.2.3

Move the negative in front of the fraction.

$y = - \frac{17}{5}$

Step 3.3

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

$(0, - \frac{17}{5})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = - \frac{17}{5} - \frac{3 (1)}{5}$

Step 4.2

Simplify $- \frac{17}{5} - \frac{3 (1)}{5}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{- 17 - 3 \cdot 1}{5}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply $- 3$ by $1$ .

$y = \frac{- 17 - 3}{5}$

Step 4.2.2.2

Subtract $3$ from $- 17$ .

$y = \frac{- 20}{5}$

Step 4.2.2.3

Divide $- 20$ by $5$ .

$y = - 4$

Step 4.3

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

$(1, - 4)$

Step 5

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

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Step 5.1

Remove parentheses.

$y = - \frac{17}{5} - \frac{3 (2)}{5}$

Step 5.2

Simplify $- \frac{17}{5} - \frac{3 (2)}{5}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{- 17 - 3 \cdot 2}{5}$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply $- 3$ by $2$ .

$y = \frac{- 17 - 6}{5}$

Step 5.2.2.2

Subtract $6$ from $- 17$ .

$y = \frac{- 23}{5}$

Step 5.2.2.3

Move the negative in front of the fraction.

$y = - \frac{23}{5}$

Step 5.3

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

$(2, - \frac{23}{5})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{17}{5}), (1, - 4), (2, - \frac{23}{5})$

Step 7