Derive Point Where Two Lines Intersect

This example demonstrates the general process for finding the point where two lines intersect, where the equations of the lines are given in the form:


  1. Start by setting the equation of the two lines equal to each other.

  2. Subtract from both sides.

  3. Subtract from both sides.

  4. Factor from the left side.

  5. Divide both sides by

    This gives us the -coordinate of the point where the lines intersect.

  6. Substitute this value into one of the equations to find the -coordinate.

    The point where the two lines intersect is .