Algebra Examples

$y - 5 = x$ $x = - 2 - y$

Step 1

Add $5$ to both sides of the equation.

$y = x + 5$

$x = - 2 - y$

Step 2

Replace all occurrences of $y$ with $x + 5$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $x = - 2 - y$ with $x + 5$ .

$x = - 2 - (x + 5)$

$y = x + 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- 2 - (x + 5)$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$x = - 2 - x - 1 \cdot 5$

$y = x + 5$

Step 2.2.1.1.2

Multiply $- 1$ by $5$ .

$x = - 2 - x - 5$

$y = x + 5$

$x = - 2 - x - 5$

$y = x + 5$

Step 2.2.1.2

Subtract $5$ from $- 2$ .

$x = - x - 7$

$y = x + 5$

$x = - x - 7$

$y = x + 5$

$x = - x - 7$

$y = x + 5$

$x = - x - 7$

$y = x + 5$

Step 3

Solve for $x$ in $x = - x - 7$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Add $x$ to both sides of the equation.

$x + x = - 7$

$y = x + 5$

Step 3.1.2

Add $x$ and $x$ .

$2 x = - 7$

$y = x + 5$

$2 x = - 7$

$y = x + 5$

Step 3.2

Divide each term in $2 x = - 7$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 x = - 7$ by $2$ .

$\frac{2 x}{2} = \frac{- 7}{2}$

$y = x + 5$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 7}{2}$

$y = x + 5$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{2}$

$y = x + 5$

$x = \frac{- 7}{2}$

$y = x + 5$

$x = \frac{- 7}{2}$

$y = x + 5$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

$y = x + 5$

$x = - \frac{7}{2}$

$y = x + 5$

$x = - \frac{7}{2}$

$y = x + 5$

$x = - \frac{7}{2}$

$y = x + 5$

Step 4

Replace all occurrences of $x$ with $- \frac{7}{2}$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = x + 5$ with $- \frac{7}{2}$ .

$y = (- \frac{7}{2}) + 5$

$x = - \frac{7}{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $(- \frac{7}{2}) + 5$ .

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Step 4.2.1.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{7}{2} + 5 \cdot \frac{2}{2}$

$x = - \frac{7}{2}$

Step 4.2.1.2

Combine $5$ and $\frac{2}{2}$ .

$y = - \frac{7}{2} + \frac{5 \cdot 2}{2}$

$x = - \frac{7}{2}$

Step 4.2.1.3

Combine the numerators over the common denominator.

$y = \frac{- 7 + 5 \cdot 2}{2}$

$x = - \frac{7}{2}$

Step 4.2.1.4

Simplify the numerator.

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Step 4.2.1.4.1

Multiply $5$ by $2$ .

$y = \frac{- 7 + 10}{2}$

$x = - \frac{7}{2}$

Step 4.2.1.4.2

Add $- 7$ and $10$ .

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

$x = - \frac{7}{2}$

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

$x = - \frac{7}{2}$

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

$x = - \frac{7}{2}$

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

$x = - \frac{7}{2}$

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

$x = - \frac{7}{2}$

Step 5

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

$(- \frac{7}{2}, \frac{3}{2})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- \frac{7}{2}, \frac{3}{2})$

Equation Form:

$x = - \frac{7}{2}, y = \frac{3}{2}$

Step 7