Solutions in a System

A system of equations is two or more equations that are graphed together on the same coordinate plane. The solution of a system of equations is the point(s) of intersection of the graphs of the equations.

  • If the equations in the system are all linear, what is the largest number of solutions possible?
  • If one of the equations is a quadratic and the rest are linear, what is the largest number of solutions possible?
  • If all of the equations are quadratic, what is the largest number of
    solutions possible?

How does the highest exponent, or the degree of the equation, relate to the largest number of solutions?

Extension:
What is the least number of equations needed to produce a solution to a system of equations with 2 variables? With N variables? Explain.

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