Pre-Algebra Examples

$2 x + 5 y = 10$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $2 x$ from both sides of the equation.

$5 y = 10 - 2 x$

Step 1.2

Divide each term in $5 y = 10 - 2 x$ by $5$ and simplify.

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Step 1.2.1

Divide each term in $5 y = 10 - 2 x$ by $5$ .

$\frac{5 y}{5} = \frac{10}{5} + \frac{- 2 x}{5}$

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.

$\frac{5 y}{5} = \frac{10}{5} + \frac{- 2 x}{5}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{10}{5} + \frac{- 2 x}{5}$

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

Divide $10$ by $5$ .

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

Step 1.2.3.1.2

Move the negative in front of the fraction.

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

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.

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

Step 3.2

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

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Cancel the common factor of $0$ and $5$ .

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Step 3.2.1.1.1

Factor $5$ out of $2 (0)$ .

$y = 2 - \frac{5 (2 \cdot (0))}{5}$

Step 3.2.1.1.2

Cancel the common factors.

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Step 3.2.1.1.2.1

Factor $5$ out of $5$ .

$y = 2 - \frac{5 (2 \cdot (0))}{5 (1)}$

Step 3.2.1.1.2.2

Cancel the common factor.

$y = 2 - \frac{5 (2 \cdot (0))}{5 \cdot 1}$

Step 3.2.1.1.2.3

Rewrite the expression.

$y = 2 - \frac{2 \cdot (0)}{1}$

Step 3.2.1.1.2.4

Divide $2 \cdot (0)$ by $1$ .

$y = 2 - (2 \cdot (0))$

Step 3.2.1.2

Multiply $- (2 \cdot (0))$ .

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Step 3.2.1.2.1

Multiply $2$ by $0$ .

$y = 2 - 0$

Step 3.2.1.2.2

Multiply $- 1$ by $0$ .

$y = 2 + 0$

Step 3.2.2

Add $2$ and $0$ .

$y = 2$

Step 3.3

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

$(0, 2)$

Step 4

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

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Step 4.1

Remove parentheses.

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

Step 4.2

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

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Step 4.2.1

Multiply $2$ by $1$ .

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

Step 4.2.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 4.2.3

Combine $2$ and $\frac{5}{5}$ .

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

Step 4.2.4

Combine the numerators over the common denominator.

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

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $2$ by $5$ .

$y = \frac{10 - 2}{5}$

Step 4.2.5.2

Subtract $2$ from $10$ .

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

Step 4.3

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

$(1, \frac{8}{5})$

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

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

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Step 5.2.1

Multiply $2$ by $2$ .

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

Step 5.2.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 5.2.3

Combine $2$ and $\frac{5}{5}$ .

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

Step 5.2.4

Combine the numerators over the common denominator.

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

Step 5.2.5

Simplify the numerator.

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Step 5.2.5.1

Multiply $2$ by $5$ .

$y = \frac{10 - 4}{5}$

Step 5.2.5.2

Subtract $4$ from $10$ .

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

Step 5.3

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

$(2, \frac{6}{5})$

Step 6

These are three possible solutions to the equation.

$(0, 2), (1, \frac{8}{5}), (2, \frac{6}{5})$

Step 7