5.1 Intro to Solving Linear-Quadratic Systems

5.1 Intro to Solving Linear-Quadratic Systems

Linear Systems can have the following types of solutions

Infinite Solutions

• Means that both equations are the same.
• Any point you pick on the line will both be a solution to the linear equations

One Solution: (-2,1)

• Both linear equations cross at one point on the graph.

No Solutions

• Means that lines do not cross. EVER

Multiple Choice

Click on the graph and determine the solutions of the system of equations.

• Infinite Solutions

• One Solutions: (3,1)

• No Solutions

• Two Solutions: 3 & 1

Multiple Choice

A system of equations when graphed are parallel to each other, determine what type of soultions they have.

• No Solution

• Infinite Solution

• One Solution

• Multiple Solutions

Fill in the Blank

An _________ solution means that the system of equations has the same equation.

Linear-Quadratic Systems can have the following types of solutions.

Two Solutions: (0,-2) and (3,1)

• System of equations cross at two points on the graph

One Solution: (1,-3)

• System of equations meet at one point on the graph

No Solution

This means that both equations NEVER intersect

Fill in the Blank

If a linear equation and a quadratic equation never intersect then the system of equation have __________.

Multiple Choice

If the a quadratic equation crosses the linear equation at two points on a graph, then the system of equations has?

• No solution

• One solution

• Two solution

• All real numbers

Multiple Choice

A linear-quadratic system touch at the point (1,-3) is said to have how many solutions?

• Two solutions

• One solution

• No solution

• Many solutions