# 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 .

Divide each term by and simplify.

Divide each term in by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .

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

Simplify the right side.

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

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

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Solve for in the second equation.

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.