Algebra Examples

$y = \frac{1}{4} x$ $x + 4 y = 8$

Step 1

Combine $\frac{1}{4}$ and $x$ .

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

$x + 4 y = 8$

Step 2

Replace all occurrences of $y$ with $\frac{x}{4}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $x + 4 y = 8$ with $\frac{x}{4}$ .

$x + 4 (\frac{x}{4}) = 8$

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $x + 4 (\frac{x}{4})$ .

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Step 2.2.1.1

Cancel the common factor of $4$ .

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Step 2.2.1.1.1

Cancel the common factor.

$x + 4 (\frac{x}{4}) = 8$

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

Step 2.2.1.1.2

Rewrite the expression.

$x + x = 8$

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

$x + x = 8$

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

Step 2.2.1.2

Add $x$ and $x$ .

$2 x = 8$

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

$2 x = 8$

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

$2 x = 8$

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

$2 x = 8$

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

Step 3

Divide each term in $2 x = 8$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 x = 8$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2}$

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{8}{2}$

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

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{2}$

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

$x = \frac{8}{2}$

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

$x = \frac{8}{2}$

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $8$ by $2$ .

$x = 4$

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

$x = 4$

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

$x = 4$

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

Step 4

Replace all occurrences of $x$ with $4$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = \frac{x}{4}$ with $4$ .

$y = \frac{4}{4}$

$x = 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

Divide $4$ by $4$ .

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(4, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 1)$

Equation Form:

$x = 4, y = 1$

Step 7