Systems of linear & quadratic equations

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),

It is just a line and a parabola together on the same graph! ('linear' and 'quadratic'):

Picture of a Quadratic and Linear System

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 System solution of system of linear equations

The 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 one solution picture

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):

Problem 1
Problem 2
Problem 3
Problem 4

Ultimate Math Solver (Free)

Free Algebra Solver ... type anything in there!