﻿ Solve Linear and Quadratic Systems. Step by Step examples with diagrams and several practice problems

# 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'):

#### 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

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

#### 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):

### Ultimate Math Solver (Free)

Free Algebra Solver ... type anything in there!