Algebra Examples

$- 8 x - 8 y = 0$ and $- 5 x - 4 y = 5$

Step 1

Solve for $x$ in $- 8 x - 8 y = 0$ .

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Step 1.1

Add $8 y$ to both sides of the equation.

$- 8 x = 8 y$

$- 5 x - 4 y = 5$

Step 1.2

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

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Step 1.2.1

Divide each term in $- 8 x = 8 y$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{8 y}{- 8}$

$- 5 x - 4 y = 5$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 8$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{8 y}{- 8}$

$- 5 x - 4 y = 5$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{8 y}{- 8}$

$- 5 x - 4 y = 5$

$x = \frac{8 y}{- 8}$

$- 5 x - 4 y = 5$

$x = \frac{8 y}{- 8}$

$- 5 x - 4 y = 5$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Cancel the common factor of $8$ and $- 8$ .

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Step 1.2.3.1.1

Factor $8$ out of $8 y$ .

$x = \frac{8 (y)}{- 8}$

$- 5 x - 4 y = 5$

Step 1.2.3.1.2

Move the negative one from the denominator of $\frac{y}{- 1}$ .

$x = - 1 \cdot y$

$- 5 x - 4 y = 5$

$x = - 1 \cdot y$

$- 5 x - 4 y = 5$

Step 1.2.3.2

Rewrite $- 1 \cdot y$ as $- y$ .

$x = - y$

$- 5 x - 4 y = 5$

$x = - y$

$- 5 x - 4 y = 5$

$x = - y$

$- 5 x - 4 y = 5$

$x = - y$

$- 5 x - 4 y = 5$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $- 5 x - 4 y = 5$ with $- y$ .

$- 5 (- y) - 4 y = 5$

$x = - y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 5 (- y) - 4 y$ .

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Step 2.2.1.1

Multiply $- 1$ by $- 5$ .

$5 y - 4 y = 5$

$x = - y$

Step 2.2.1.2

Subtract $4 y$ from $5 y$ .

$y = 5$

$x = - y$

$y = 5$

$x = - y$

$y = 5$

$x = - y$

$y = 5$

$x = - y$

Step 3

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

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Step 3.1

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

$x = - (5)$

$y = 5$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 1$ by $5$ .

$x = - 5$

$y = 5$

$x = - 5$

$y = 5$

$x = - 5$

$y = 5$

Step 4

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

$(- 5, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 5, 5)$

Equation Form:

$x = - 5, y = 5$

Step 6