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.
The same thing is true for a linear quadratic system. The solution is where the parabola and the line 'meet'
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
Graph of a system with one solution
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):
