# 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.

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

Subtract from both sides of the equation.

Subtract from .

Subtract from both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Simplify the left side of the by cancelling the common factors.

Reduce the expression by cancelling the common factors.

Factor out of .

Move the negative one from the denominator of .

Simplify the expression.

Multiply by .

Rewrite as .

Divide by .

Solve for in the first equation.

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Multiply by .

Solve for in the second equation.

List the solutions to the system of equations.

The solution to the system of equations can be represented as a point.

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