Algebra Examples

$y = \frac{1}{2} x - 6$ $y = - x$

Step 1

Eliminate the equal sides of each equation and combine.

$\frac{1}{2} x - 6 = - x$

Step 2

Solve $\frac{1}{2} x - 6 = - x$ for $x$ .

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

Add $x$ to both sides of the equation.

$\frac{x}{2} - 6 + x = 0$

Step 2.2.2

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

$\frac{x}{2} + x \cdot \frac{2}{2} - 6 = 0$

Step 2.2.3

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

$\frac{x}{2} + \frac{x \cdot 2}{2} - 6 = 0$

Step 2.2.4

Combine the numerators over the common denominator.

$\frac{x + x \cdot 2}{2} - 6 = 0$

Step 2.2.5

Add $x$ and $x \cdot 2$ .

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Step 2.2.5.1

Reorder $x$ and $2$ .

$\frac{x + 2 \cdot x}{2} - 6 = 0$

Step 2.2.5.2

Add $x$ and $2 \cdot x$ .

$\frac{3 x}{2} - 6 = 0$

Step 2.3

Add $6$ to both sides of the equation.

$\frac{3 x}{2} = 6$

Step 2.4

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot 6$

Step 2.5

Simplify both sides of the equation.

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Step 2.5.1

Simplify the left side.

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Step 2.5.1.1

Simplify $\frac{2}{3} \cdot \frac{3 x}{2}$ .

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Step 2.5.1.1.1

Cancel the common factor of $2$ .

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Step 2.5.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot 6$

Step 2.5.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot 6$

Step 2.5.1.1.2

Cancel the common factor of $3$ .

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Step 2.5.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{2}{3} \cdot 6$

Step 2.5.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot 6$

Step 2.5.1.1.2.3

Rewrite the expression.

$x = \frac{2}{3} \cdot 6$

Step 2.5.2

Simplify the right side.

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Step 2.5.2.1

Simplify $\frac{2}{3} \cdot 6$ .

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Step 2.5.2.1.1

Cancel the common factor of $3$ .

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Step 2.5.2.1.1.1

Factor $3$ out of $6$ .

$x = \frac{2}{3} \cdot (3 (2))$

Step 2.5.2.1.1.2

Cancel the common factor.

$x = \frac{2}{3} \cdot (3 \cdot 2)$

Step 2.5.2.1.1.3

Rewrite the expression.

$x = 2 \cdot 2$

Step 2.5.2.1.2

Multiply $2$ by $2$ .

$x = 4$

Step 3

Evaluate $y$ when $x = 4$ .

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Step 3.1

Substitute $4$ for $x$ .

$y = - (4)$

Step 3.2

Multiply $- 1$ by $4$ .

$y = - 4$

Step 4

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

$(4, - 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, - 4)$

Equation Form:

$x = 4, y = - 4$

Step 6