Pre-Algebra Examples

$5 y = 2 x - 3$

Step 1

Divide each term in $5 y = 2 x - 3$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 y = 2 x - 3$ by $5$ .

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

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

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

Step 1.2.1.2

Divide $y$ by $1$ .

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

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative in front of the fraction.

$y = \frac{2 x}{5} - \frac{3}{5}$

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.

$y = \frac{2 (0)}{5} - \frac{3}{5}$

Step 3.2

Simplify $\frac{2 (0)}{5} - \frac{3}{5}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{2 (0) - 3}{5}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $2$ by $0$ .

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

Step 3.2.2.2

Subtract $3$ from $0$ .

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

Step 3.2.2.3

Move the negative in front of the fraction.

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

Step 3.3

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

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

Step 4

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

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Step 4.1

Remove parentheses.

$y = \frac{2 (1)}{5} - \frac{3}{5}$

Step 4.2

Simplify $\frac{2 (1)}{5} - \frac{3}{5}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{2 (1) - 3}{5}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply $2$ by $1$ .

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

Step 4.2.2.2

Subtract $3$ from $2$ .

$y = \frac{- 1}{5}$

Step 4.2.2.3

Move the negative in front of the fraction.

$y = - \frac{1}{5}$

Step 4.3

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

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

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

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

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Step 5.2.1

Combine the numerators over the common denominator.

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

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply $2$ by $2$ .

$y = \frac{4 - 3}{5}$

Step 5.2.2.2

Subtract $3$ from $4$ .

$y = \frac{1}{5}$

Step 5.3

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

$(2, \frac{1}{5})$

Step 6

These are three possible solutions to the equation.

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

Step 7