# Algebra 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.

Since contains the variable to solve for, move it to the left side of the equation by subtracting from both sides.

Subtract from to get .

Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.

Divide each term by and simplify.

Divide each term in by .

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

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative one from the denominator of .

Simplify the expression.

Multiply by to get .

Rewrite as .

Divide by to get .

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

Multiply by to get .

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.