# Algebra Examples

,

Step 1

Step 1.1

The slope-intercept form is , where is the slope and is the y-intercept.

Step 1.2

Using the slope-intercept form, the slope is .

Step 2

Step 2.1

The slope-intercept form is , where is the slope and is the y-intercept.

Step 2.2

Using the slope-intercept form, the slope is .

Step 3

Set up the system of equations to find any points of intersection.

Step 4

Step 4.1

Eliminate the equal sides of each equation and combine.

Step 4.2

Solve for .

Step 4.2.1

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

Step 4.2.1.1

Subtract from both sides of the equation.

Step 4.2.1.2

Subtract from .

Step 4.2.2

Divide each term in by and simplify.

Step 4.2.2.1

Divide each term in by .

Step 4.2.2.2

Simplify the left side.

Step 4.2.2.2.1

Cancel the common factor of .

Step 4.2.2.2.1.1

Cancel the common factor.

Step 4.2.2.2.1.2

Divide by .

Step 4.3

Evaluate when .

Step 4.3.1

Substitute for .

Step 4.3.2

Substitute for in and solve for .

Step 4.3.2.1

Remove parentheses.

Step 4.3.2.2

Remove parentheses.

Step 4.3.2.3

Simplify .

Step 4.3.2.3.1

To write as a fraction with a common denominator, multiply by .

Step 4.3.2.3.2

Combine and .

Step 4.3.2.3.3

Combine the numerators over the common denominator.

Step 4.3.2.3.4

Simplify the numerator.

Step 4.3.2.3.4.1

Multiply by .

Step 4.3.2.3.4.2

Add and .

Step 4.4

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

Step 5

Since the slopes are different, the lines will have exactly one intersection point.

Step 6