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),
![](../algebra/linear_equation/systems-of-equation/images/icon-system-of-equations2.png)
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 system of linear equations](../algebra/linear_equation/systems-of-equation/images/solutions-systems-linear-equations/solution-icon.png)
The same thing is true for a linear quadratic system. The solution is where the parabola and the line 'meet'
![one solution picture](images/one-solution-picture.png)
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.
System with two real solutions
![](images/two-solutions-picture.gif)
Graph of a system with one solution
![](images/one-solution-picture.gif)
Graph of a system with No real solutions
![](images/no-real-solutions-picture.gif)
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):