Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and the other is quadratic–without graphing the system of equations.

Answer:

Isolate one variable in the system of equations. Use substitution to create a onevariable equation. Then, set the quadratic equation equal to zero and find the discriminant. If the discriminant is negative, then there are no real number solutions. If the discriminant is zero, then there is one real number solution. If the discriminant is positive, then there are two real number solutions.