# Precalculus Examples

,

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

Using the slope-intercept form, the slope is .

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

Using the slope-intercept form, the slope is .

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

Eliminate the equal sides of each equation and combine.

Solve for .

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

Subtract from both sides of the equation.

Subtract from .

Add to both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Evaluate when .

Substitute for .

Multiply by .

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

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