Algebra Examples

$y = - x$ $y = \frac{2}{5} x - 7$

Step 1

Eliminate the equal sides of each equation and combine.

$- x = \frac{2}{5} x - 7$

Step 2

Solve $- x = \frac{2}{5} x - 7$ for $x$ .

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Step 2.1

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

$- x = \frac{2 x}{5} - 7$

Step 2.2

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

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Step 2.2.1

Subtract $\frac{2 x}{5}$ from both sides of the equation.

$- x - \frac{2 x}{5} = - 7$

Step 2.2.2

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

$- x \cdot \frac{5}{5} - \frac{2 x}{5} = - 7$

Step 2.2.3

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

$\frac{- x \cdot 5}{5} - \frac{2 x}{5} = - 7$

Step 2.2.4

Combine the numerators over the common denominator.

$\frac{- x \cdot 5 - 2 x}{5} = - 7$

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Factor $x$ out of $- x \cdot 5 - 2 x$ .

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Step 2.2.5.1.1

Factor $x$ out of $- x \cdot 5$ .

$\frac{x (- 1 \cdot 5) - 2 x}{5} = - 7$

Step 2.2.5.1.2

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

$\frac{x (- 1 \cdot 5) + x \cdot - 2}{5} = - 7$

Step 2.2.5.1.3

Factor $x$ out of $x (- 1 \cdot 5) + x \cdot - 2$ .

$\frac{x (- 1 \cdot 5 - 2)}{5} = - 7$

Step 2.2.5.2

Multiply $- 1$ by $5$ .

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

Step 2.2.5.3

Subtract $2$ from $- 5$ .

$\frac{x \cdot - 7}{5} = - 7$

Step 2.2.6

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{5} = - 7$

Step 2.2.7

Move the negative in front of the fraction.

$- \frac{7 x}{5} = - 7$

Step 2.3

Multiply both sides of the equation by $- \frac{5}{7}$ .

$- \frac{5}{7} (- \frac{7 x}{5}) = - \frac{5}{7} \cdot - 7$

Step 2.4

Simplify both sides of the equation.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

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

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Step 2.4.1.1.1

Cancel the common factor of $5$ .

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Step 2.4.1.1.1.1

Move the leading negative in $- \frac{5}{7}$ into the numerator.

$\frac{- 5}{7} (- \frac{7 x}{5}) = - \frac{5}{7} \cdot - 7$

Step 2.4.1.1.1.2

Move the leading negative in $- \frac{7 x}{5}$ into the numerator.

$\frac{- 5}{7} \cdot \frac{- 7 x}{5} = - \frac{5}{7} \cdot - 7$

Step 2.4.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{7} \cdot \frac{- 7 x}{5} = - \frac{5}{7} \cdot - 7$

Step 2.4.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{7} \cdot \frac{- 7 x}{5} = - \frac{5}{7} \cdot - 7$

Step 2.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) = - \frac{5}{7} \cdot - 7$

Step 2.4.1.1.2

Cancel the common factor of $7$ .

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Step 2.4.1.1.2.1

Factor $7$ out of $- 7 x$ .

$\frac{- 1}{7} (7 (- x)) = - \frac{5}{7} \cdot - 7$

Step 2.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) = - \frac{5}{7} \cdot - 7$

Step 2.4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{5}{7} \cdot - 7$

Step 2.4.1.1.3

Multiply.

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Step 2.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{5}{7} \cdot - 7$

Step 2.4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{5}{7} \cdot - 7$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Simplify $- \frac{5}{7} \cdot - 7$ .

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Step 2.4.2.1.1

Cancel the common factor of $7$ .

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Step 2.4.2.1.1.1

Move the leading negative in $- \frac{5}{7}$ into the numerator.

$x = \frac{- 5}{7} \cdot - 7$

Step 2.4.2.1.1.2

Factor $7$ out of $- 7$ .

$x = \frac{- 5}{7} \cdot (7 (- 1))$

Step 2.4.2.1.1.3

Cancel the common factor.

$x = \frac{- 5}{7} \cdot (7 \cdot - 1)$

Step 2.4.2.1.1.4

Rewrite the expression.

$x = - 5 \cdot - 1$

Step 2.4.2.1.2

Multiply $- 5$ by $- 1$ .

$x = 5$

Step 3

Evaluate $y$ when $x = 5$ .

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Step 3.1

Substitute $5$ for $x$ .

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

Step 3.2

Substitute $5$ for $x$ in $y = \frac{2}{5} \cdot (5) - 7$ and solve for $y$ .

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Step 3.2.1

Multiply $\frac{2}{5}$ by $5$ .

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

Step 3.2.2

Simplify $\frac{2}{5} \cdot 5 - 7$ .

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.1.2

Rewrite the expression.

$y = 2 - 7$

Step 3.2.2.2

Subtract $7$ from $2$ .

$y = - 5$

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