Algebra Examples

$5 y = 2 - 6 x$ $y - 2 x = 10$

Step 1

Divide each term in $5 y = 2 - 6 x$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 y = 2 - 6 x$ by $5$ .

$\frac{5 y}{5} = \frac{2}{5} + \frac{- 6 x}{5}$

$y - 2 x = 10$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{2}{5} + \frac{- 6 x}{5}$

$y - 2 x = 10$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{2}{5} + \frac{- 6 x}{5}$

$y - 2 x = 10$

$y = \frac{2}{5} + \frac{- 6 x}{5}$

$y - 2 x = 10$

$y = \frac{2}{5} + \frac{- 6 x}{5}$

$y - 2 x = 10$

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative in front of the fraction.

$y = \frac{2}{5} - \frac{6 x}{5}$

$y - 2 x = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

$y - 2 x = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

$y - 2 x = 10$

Step 2

Replace all occurrences of $y$ with $\frac{2}{5} - \frac{6 x}{5}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $y - 2 x = 10$ with $\frac{2}{5} - \frac{6 x}{5}$ .

$(\frac{2}{5} - \frac{6 x}{5}) - 2 x = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $(\frac{2}{5} - \frac{6 x}{5}) - 2 x$ .

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Step 2.2.1.1

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

$\frac{2}{5} - \frac{6 x}{5} - 2 x \cdot \frac{5}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 2.2.1.2

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

$\frac{2}{5} - \frac{6 x}{5} + \frac{- 2 x \cdot 5}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 2.2.1.3

Combine the numerators over the common denominator.

$\frac{2}{5} + \frac{- 6 x - 2 x \cdot 5}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 2.2.1.4

Combine the numerators over the common denominator.

$\frac{2 - 6 x - 2 x \cdot 5}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 2.2.1.5

Multiply $5$ by $- 2$ .

$\frac{2 - 6 x - 10 x}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 2.2.1.6

Subtract $10 x$ from $- 6 x$ .

$\frac{2 - 16 x}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 2.2.1.7

Factor $2$ out of $2 - 16 x$ .

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Step 2.2.1.7.1

Factor $2$ out of $2$ .

$\frac{2 (1) - 16 x}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 2.2.1.7.2

Factor $2$ out of $- 16 x$ .

$\frac{2 (1) + 2 (- 8 x)}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 2.2.1.7.3

Factor $2$ out of $2 (1) + 2 (- 8 x)$ .

$\frac{2 (1 - 8 x)}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

$\frac{2 (1 - 8 x)}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

$\frac{2 (1 - 8 x)}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

$\frac{2 (1 - 8 x)}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

$\frac{2 (1 - 8 x)}{5} = 10$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3

Solve for $x$ in $\frac{2 (1 - 8 x)}{5} = 10$ .

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Step 3.1

Multiply both sides by $5$ .

$\frac{2 (1 - 8 x)}{5} \cdot 5 = 10 \cdot 5$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $\frac{2 (1 - 8 x)}{5} \cdot 5$ .

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Step 3.2.1.1.1

Cancel the common factor of $5$ .

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Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{2 (1 - 8 x)}{5} \cdot 5 = 10 \cdot 5$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.2.1.1.1.2

Rewrite the expression.

$2 (1 - 8 x) = 10 \cdot 5$

$y = \frac{2}{5} - \frac{6 x}{5}$

$2 (1 - 8 x) = 10 \cdot 5$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.2.1.1.2

Apply the distributive property.

$2 \cdot 1 + 2 (- 8 x) = 10 \cdot 5$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.2.1.1.3

Simplify the expression.

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Step 3.2.1.1.3.1

Multiply $2$ by $1$ .

$2 + 2 (- 8 x) = 10 \cdot 5$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.2.1.1.3.2

Multiply $- 8$ by $2$ .

$2 - 16 x = 10 \cdot 5$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.2.1.1.3.3

Reorder $2$ and $- 16 x$ .

$- 16 x + 2 = 10 \cdot 5$

$y = \frac{2}{5} - \frac{6 x}{5}$

$- 16 x + 2 = 10 \cdot 5$

$y = \frac{2}{5} - \frac{6 x}{5}$

$- 16 x + 2 = 10 \cdot 5$

$y = \frac{2}{5} - \frac{6 x}{5}$

$- 16 x + 2 = 10 \cdot 5$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $10$ by $5$ .

$- 16 x + 2 = 50$

$y = \frac{2}{5} - \frac{6 x}{5}$

$- 16 x + 2 = 50$

$y = \frac{2}{5} - \frac{6 x}{5}$

$- 16 x + 2 = 50$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.3

Solve for $x$ .

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Step 3.3.1

Move all terms not containing $x$ to the right side of the equation.

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Step 3.3.1.1

Subtract $2$ from both sides of the equation.

$- 16 x = 50 - 2$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.3.1.2

Subtract $2$ from $50$ .

$- 16 x = 48$

$y = \frac{2}{5} - \frac{6 x}{5}$

$- 16 x = 48$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.3.2

Divide each term in $- 16 x = 48$ by $- 16$ and simplify.

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Step 3.3.2.1

Divide each term in $- 16 x = 48$ by $- 16$ .

$\frac{- 16 x}{- 16} = \frac{48}{- 16}$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.3.2.2

Simplify the left side.

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Step 3.3.2.2.1

Cancel the common factor of $- 16$ .

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Step 3.3.2.2.1.1

Cancel the common factor.

$\frac{- 16 x}{- 16} = \frac{48}{- 16}$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{48}{- 16}$

$y = \frac{2}{5} - \frac{6 x}{5}$

$x = \frac{48}{- 16}$

$y = \frac{2}{5} - \frac{6 x}{5}$

$x = \frac{48}{- 16}$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 3.3.2.3

Simplify the right side.

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Step 3.3.2.3.1

Divide $48$ by $- 16$ .

$x = - 3$

$y = \frac{2}{5} - \frac{6 x}{5}$

$x = - 3$

$y = \frac{2}{5} - \frac{6 x}{5}$

$x = - 3$

$y = \frac{2}{5} - \frac{6 x}{5}$

$x = - 3$

$y = \frac{2}{5} - \frac{6 x}{5}$

$x = - 3$

$y = \frac{2}{5} - \frac{6 x}{5}$

Step 4

Replace all occurrences of $x$ with $- 3$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = \frac{2}{5} - \frac{6 x}{5}$ with $- 3$ .

$y = \frac{2}{5} - \frac{6 (- 3)}{5}$

$x = - 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{2}{5} - \frac{6 (- 3)}{5}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$y = \frac{2 - 6 \cdot - 3}{5}$

$x = - 3$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Multiply $- 6$ by $- 3$ .

$y = \frac{2 + 18}{5}$

$x = - 3$

Step 4.2.1.2.2

Add $2$ and $18$ .

$y = \frac{20}{5}$

$x = - 3$

Step 4.2.1.2.3

Divide $20$ by $5$ .

$y = 4$

$x = - 3$

$y = 4$

$x = - 3$

$y = 4$

$x = - 3$

$y = 4$

$x = - 3$

$y = 4$

$x = - 3$

Step 5

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

$(- 3, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 3, 4)$

Equation Form:

$x = - 3, y = 4$

Step 7