Pre-Algebra Examples

$5 x + 10 + 3 y = 25$

Step 1

Solve the equation for $y$ .

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Step 1.1

Move all terms not containing $y$ to the right side of the equation.

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Step 1.1.1

Subtract $5 x$ from both sides of the equation.

$10 + 3 y = 25 - 5 x$

Step 1.1.2

Subtract $10$ from both sides of the equation.

$3 y = 25 - 5 x - 10$

Step 1.1.3

Subtract $10$ from $25$ .

$3 y = - 5 x + 15$

Step 1.2

Divide each term in $3 y = - 5 x + 15$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 y = - 5 x + 15$ by $3$ .

$\frac{3 y}{3} = \frac{- 5 x}{3} + \frac{15}{3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 5 x}{3} + \frac{15}{3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 5 x}{3} + \frac{15}{3}$

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.

$y = - \frac{5 x}{3} + \frac{15}{3}$

Step 1.2.3.1.2

Divide $15$ by $3$ .

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

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.

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

Step 3.2

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

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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 $3$ .

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Step 3.2.1.1.1

Factor $3$ out of $5 (0)$ .

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

Step 3.2.1.1.2

Cancel the common factors.

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Step 3.2.1.1.2.1

Factor $3$ out of $3$ .

$y = - \frac{3 (5 \cdot (0))}{3 (1)} + 5$

Step 3.2.1.1.2.2

Cancel the common factor.

$y = - \frac{3 (5 \cdot (0))}{3 \cdot 1} + 5$

Step 3.2.1.1.2.3

Rewrite the expression.

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

Step 3.2.1.1.2.4

Divide $5 \cdot (0)$ by $1$ .

$y = - (5 \cdot (0)) + 5$

Step 3.2.1.2

Multiply $- (5 \cdot (0))$ .

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Step 3.2.1.2.1

Multiply $5$ by $0$ .

$y = - 0 + 5$

Step 3.2.1.2.2

Multiply $- 1$ by $0$ .

$y = 0 + 5$

Step 3.2.2

Add $0$ and $5$ .

$y = 5$

Step 3.3

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

$(0, 5)$

Step 4

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

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Step 4.1

Remove parentheses.

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

Step 4.2

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

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Step 4.2.1

Multiply $5$ by $1$ .

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

Step 4.2.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{5}{3} + 5 \cdot \frac{3}{3}$

Step 4.2.3

Combine $5$ and $\frac{3}{3}$ .

$y = - \frac{5}{3} + \frac{5 \cdot 3}{3}$

Step 4.2.4

Combine the numerators over the common denominator.

$y = \frac{- 5 + 5 \cdot 3}{3}$

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $5$ by $3$ .

$y = \frac{- 5 + 15}{3}$

Step 4.2.5.2

Add $- 5$ and $15$ .

$y = \frac{10}{3}$

Step 4.3

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

$(1, \frac{10}{3})$

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

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

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Step 5.2.1

Multiply $5$ by $2$ .

$y = - \frac{10}{3} + 5$

Step 5.2.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{10}{3} + 5 \cdot \frac{3}{3}$

Step 5.2.3

Combine $5$ and $\frac{3}{3}$ .

$y = - \frac{10}{3} + \frac{5 \cdot 3}{3}$

Step 5.2.4

Combine the numerators over the common denominator.

$y = \frac{- 10 + 5 \cdot 3}{3}$

Step 5.2.5

Simplify the numerator.

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Step 5.2.5.1

Multiply $5$ by $3$ .

$y = \frac{- 10 + 15}{3}$

Step 5.2.5.2

Add $- 10$ and $15$ .

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

Step 5.3

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

$(2, \frac{5}{3})$

Step 6

These are three possible solutions to the equation.

$(0, 5), (1, \frac{10}{3}), (2, \frac{5}{3})$

Step 7