Algebra Examples

$\frac{1}{2} (2 x + y) = \frac{21}{2}$ $y = 2 x$

Step 1

Replace all occurrences of $y$ with $2 x$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $x + \frac{y}{2} = \frac{21}{2}$ with $2 x$ .

$x + \frac{2 x}{2} = \frac{21}{2}$

$y = 2 x$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $x + \frac{2 x}{2}$ .

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Step 1.2.1.1

Cancel the common factor of $2$ .

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Step 1.2.1.1.1

Cancel the common factor.

$x + \frac{2 x}{2} = \frac{21}{2}$

$y = 2 x$

Step 1.2.1.1.2

Divide $x$ by $1$ .

$x + x = \frac{21}{2}$

$y = 2 x$

$x + x = \frac{21}{2}$

$y = 2 x$

Step 1.2.1.2

Add $x$ and $x$ .

$2 x = \frac{21}{2}$

$y = 2 x$

$2 x = \frac{21}{2}$

$y = 2 x$

$2 x = \frac{21}{2}$

$y = 2 x$

$2 x = \frac{21}{2}$

$y = 2 x$

Step 2

Divide each term in $2 x = \frac{21}{2}$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 x = \frac{21}{2}$ by $2$ .

$\frac{2 x}{2} = \frac{\frac{21}{2}}{2}$

$y = 2 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{\frac{21}{2}}{2}$

$y = 2 x$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{21}{2}}{2}$

$y = 2 x$

$x = \frac{\frac{21}{2}}{2}$

$y = 2 x$

$x = \frac{\frac{21}{2}}{2}$

$y = 2 x$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{21}{2} \cdot \frac{1}{2}$

$y = 2 x$

Step 2.3.2

Multiply $\frac{21}{2} \cdot \frac{1}{2}$ .

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Step 2.3.2.1

Multiply $\frac{21}{2}$ by $\frac{1}{2}$ .

$x = \frac{21}{2 \cdot 2}$

$y = 2 x$

Step 2.3.2.2

Multiply $2$ by $2$ .

$x = \frac{21}{4}$

$y = 2 x$

$x = \frac{21}{4}$

$y = 2 x$

$x = \frac{21}{4}$

$y = 2 x$

$x = \frac{21}{4}$

$y = 2 x$

Step 3

Replace all occurrences of $x$ with $\frac{21}{4}$ in each equation.

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Step 3.1

Replace all occurrences of $x$ in $y = 2 x$ with $\frac{21}{4}$ .

$y = 2 (\frac{21}{4})$

$x = \frac{21}{4}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Factor $2$ out of $4$ .

$y = 2 (\frac{21}{2 (2)})$

$x = \frac{21}{4}$

Step 3.2.1.2

Cancel the common factor.

$y = 2 (\frac{21}{2 \cdot 2})$

$x = \frac{21}{4}$

Step 3.2.1.3

Rewrite the expression.

$y = \frac{21}{2}$

$x = \frac{21}{4}$

$y = \frac{21}{2}$

$x = \frac{21}{4}$

$y = \frac{21}{2}$

$x = \frac{21}{4}$

$y = \frac{21}{2}$

$x = \frac{21}{4}$

Step 4

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

$(\frac{21}{4}, \frac{21}{2})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(\frac{21}{4}, \frac{21}{2})$

Equation Form:

$x = \frac{21}{4}, y = \frac{21}{2}$

Step 6