Algebra Examples

$y = - \frac{1}{2} x$ $2 x + 2 y = 5$

Step 1

Combine $x$ and $\frac{1}{2}$ .

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

$2 x + 2 y = 5$

Step 2

Replace all occurrences of $y$ with $- \frac{x}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $2 x + 2 y = 5$ with $- \frac{x}{2}$ .

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

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

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

Step 2.2.1.1.2

Cancel the common factor.

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

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

Step 2.2.1.1.3

Rewrite the expression.

$2 x - x = 5$

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

$2 x - x = 5$

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

Step 2.2.1.2

Subtract $x$ from $2 x$ .

$x = 5$

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

$x = 5$

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

$x = 5$

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

$x = 5$

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

Step 3

Replace all occurrences of $x$ in $y = - \frac{x}{2}$ with $5$ .

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

$x = 5$

Step 4

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

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

Step 5

The result can be shown in multiple forms.

Point Form:

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

Equation Form:

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

Step 6