Question

identifying the number of solutions of a system of equations
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.

Explanation:

Answer:

Substitute the linear equation into the quadratic equation to form a single quadratic equation \(ax^{2}+bx + c = 0\). Then use the discriminant \(D=b^{2}-4ac\). If \(D>0\), there are two real - number solutions. If \(D = 0\), there is one real - number solution. If \(D<0\), there are no real - number solutions.