Question

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 1

Answer:

To determine the number of real number solutions of as system of equations in which one equation is linear and the other is quadratic

1) Given that there are two variables, x and y as an example, we make y the subject of the equation of the linear equation and substitute the the expression for y in x into the quadratic equation

We simplify and check the number of real roots with the quadratic formula, $x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}$ for quadratic equations  the form 0 = a·x² - b·x + c

Where b² > 4·a·c there are two possible solutions and when b² = 4·a·c equation there is only one solution.

Step-by-step explanation: