#### What is a linear and quadratic system anyway?

Just like a system of linear equations means 'more than 1 line ' on a graph (see picture on right),

#### Ok, so what is the __solution__ of a system of equations?

The solution is where the equations 'meet' or intersect. The red point on the right is the solution of a system of linear equations.

**Solution of a**

__Linear__SystemThe same thing is true for a linear quadratic system. The solution is where the parabola and the line 'meet'

**Solution of A**

__Linear Quadratic__System#### How many solutions can a linear and Quadratic

System Have?

A system of a linear equation and a quadratic equation can have one real solution, two real solutions or no real solutions.

**Two Real Solutions<**

System with two real solutions

**One Real Solution**

Graph of a system with one solution

**No Real Solutions**

Graph of a system with No real solutions

#### How can you solve linear and Quadratic Systems?

Just like systems of linear equations, you can solve linear quadratic systems both algebraically and graphically. We will use the algebraic method , on this page.

**Practice** Problems

**Directions:**Solve the linear quadratic system below (algebraically):