Algebra Examples

$y = \frac{1}{3} x + 6$ $y = \frac{1}{6} x + 5$

Step 1

Eliminate the equal sides of each equation and combine.

$\frac{1}{3} x + 6 = \frac{1}{6} x + 5$

Step 2

Solve $\frac{1}{3} x + 6 = \frac{1}{6} x + 5$ for $x$ .

Tap for more steps...

Step 2.1

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} + 6 = \frac{1}{6} x + 5$

Step 2.2

Combine $\frac{1}{6}$ and $x$ .

$\frac{x}{3} + 6 = \frac{x}{6} + 5$

Step 2.3

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

Tap for more steps...

Step 2.3.1

Subtract $\frac{x}{6}$ from both sides of the equation.

$\frac{x}{3} + 6 - \frac{x}{6} = 5$

Step 2.3.2

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.3.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.3.3.1

Multiply $\frac{x}{3}$ by $\frac{2}{2}$ .

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

Step 2.3.3.2

Multiply $3$ by $2$ .

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

Step 2.3.4

Combine the numerators over the common denominator.

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

Step 2.3.5

Subtract $x$ from $x \cdot 2$ .

Tap for more steps...

Step 2.3.5.1

Reorder $x$ and $2$ .

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

Step 2.3.5.2

Subtract $x$ from $2 \cdot x$ .

$\frac{x}{6} + 6 = 5$

Step 2.4

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

Tap for more steps...

Step 2.4.1

Subtract $6$ from both sides of the equation.

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

Step 2.4.2

Subtract $6$ from $5$ .

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

Step 2.5

Multiply both sides of the equation by $6$ .

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

Step 2.6

Simplify both sides of the equation.

Tap for more steps...

Step 2.6.1

Simplify the left side.

Tap for more steps...

Step 2.6.1.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 2.6.1.1.1

Cancel the common factor.

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

Step 2.6.1.1.2

Rewrite the expression.

$x = 6 \cdot - 1$

Step 2.6.2

Simplify the right side.

Tap for more steps...

Step 2.6.2.1

Multiply $6$ by $- 1$ .

$x = - 6$

Step 3

Evaluate $y$ when $x = - 6$ .

Tap for more steps...

Step 3.1

Substitute $- 6$ for $x$ .

$y = \frac{1}{6} \cdot (- 6) + 5$

Step 3.2

Substitute $- 6$ for $x$ in $y = \frac{1}{6} \cdot (- 6) + 5$ and solve for $y$ .

Tap for more steps...

Step 3.2.1

Multiply $\frac{1}{6}$ by $- 6$ .

$y = \frac{1}{6} \cdot - 6 + 5$

Step 3.2.2

Simplify $\frac{1}{6} \cdot - 6 + 5$ .

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 3.2.2.1.1

Factor $6$ out of $- 6$ .

$y = \frac{1}{6} \cdot (6 (- 1)) + 5$

Step 3.2.2.1.2

Cancel the common factor.

$y = \frac{1}{6} \cdot (6 \cdot - 1) + 5$

Step 3.2.2.1.3

Rewrite the expression.

$y = - 1 + 5$

Step 3.2.2.2

Add $- 1$ and $5$ .

$y = 4$

Step 4

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

$(- 6, 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 6, 4)$

Equation Form:

$x = - 6, y = 4$

Step 6