Pre-Algebra Examples

$\frac{x}{4} + \frac{y}{4} = 1$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $\frac{x}{4}$ from both sides of the equation.

$\frac{y}{4} = 1 - \frac{x}{4}$

Step 1.2

Multiply both sides of the equation by $4$ .

$4 \frac{y}{4} = 4 (1 - \frac{x}{4})$

Step 1.3

Simplify both sides of the equation.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Cancel the common factor of $4$ .

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Step 1.3.1.1.1

Cancel the common factor.

$4 \frac{y}{4} = 4 (1 - \frac{x}{4})$

Step 1.3.1.1.2

Rewrite the expression.

$y = 4 (1 - \frac{x}{4})$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $4 (1 - \frac{x}{4})$ .

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Step 1.3.2.1.1

Apply the distributive property.

$y = 4 \cdot 1 + 4 (- \frac{x}{4})$

Step 1.3.2.1.2

Multiply $4$ by $1$ .

$y = 4 + 4 (- \frac{x}{4})$

Step 1.3.2.1.3

Cancel the common factor of $4$ .

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Step 1.3.2.1.3.1

Move the leading negative in $- \frac{x}{4}$ into the numerator.

$y = 4 + 4 \frac{- x}{4}$

Step 1.3.2.1.3.2

Cancel the common factor.

$y = 4 + 4 \frac{- x}{4}$

Step 1.3.2.1.3.3

Rewrite the expression.

$y = 4 - x$

Step 1.4

Reorder $4$ and $- x$ .

$y = - x + 4$

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.

$y = - (0) + 4$

Step 3.2

Simplify $- (0) + 4$ .

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Step 3.2.1

Multiply $- 1$ by $0$ .

$y = 0 + 4$

Step 3.2.2

Add $0$ and $4$ .

$y = 4$

Step 3.3

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

$(0, 4)$

Step 4

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

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Step 4.1

Remove parentheses.

$y = - (1) + 4$

Step 4.2

Simplify $- (1) + 4$ .

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Step 4.2.1

Multiply $- 1$ by $1$ .

$y = - 1 + 4$

Step 4.2.2

Add $- 1$ and $4$ .

$y = 3$

Step 4.3

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

$(1, 3)$

Step 5

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

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Step 5.1

Remove parentheses.

$y = - (2) + 4$

Step 5.2

Simplify $- (2) + 4$ .

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Step 5.2.1

Multiply $- 1$ by $2$ .

$y = - 2 + 4$

Step 5.2.2

Add $- 2$ and $4$ .

$y = 2$

Step 5.3

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

$(2, 2)$

Step 6

These are three possible solutions to the equation.

$(0, 4), (1, 3), (2, 2)$

Step 7