##### 7.1 System of linear-quadratic equations

By now we are already familiar with two different kinds of equations: the linear equation andthe quadratic equation. Linear equations have two variables x and y, those that have the general formula of Ax + By + C = 0. Quadratic Equations on the other hand have one variable and has a formula $Ax^2 + Bx + C = 0$.

In this chapter we will talk about system of equations. From previous chapter, we were able to learn about Linear Systems which is just a part of the system of equations. In this chapter we will look at the other system of equations like the quadratic system. We will also learn that systems of equations aren’t just collection of linear or quadratic equations, but it can also be a combination of both, some systems are linear-quadratic equations and quadratic-quadratic equations.

We will also take a look at the graphs of a system of equations. Graphically, we would be able to understand systems of equation. If you would remember, the graphs of linear equations are straight lines and the quadratic equations are parabolas. In this chapter, since we will be dealing with linear-quadratic and quadratic-quadratic equation, we would learn how to graphically understand the system of equations. We will also learn how to solve system of equations graphically and in the process, learn how to find the points of intersection both graphically and algebraically.

### System of linear-quadratic equations

The solutions to a system of equations are the points of intersection of their graphs. There are 3 cases you will come across when trying to solve the system. There can be 2 solutions, 1 solution or even no solutions.