Number of Solutions of Linear Equations

3.1 - Solve Systems of Linear Equations by Graphing

Objective

To solve a linear system using a graph or a table.

Vocabulary

​Solution

A solution to an equation is the value of the variable that makes the equation true.

​In this unit we are going to be solving systems of linear equations.

A system of equations is two or more equations containing two or more variables.

​So can a system of equations have a solution?

Yes!

Solution to a System of Equations

The set of all points that satisfy each equation. In most cases this is the one point that makes both equations true.

There are three types of solutions

​One Solution	​No Solution	​Infinitely Many Solutions
​(Lines intersect)	​(Lines are parallel)	​(Same line)

​We will learn three methods to solve systems of linear equations.

The first is solving by graphing. We will graph both equations on the same coordinate plane. The point where they cross (called "the point of intersection") is the solution to the system.

Let's practice one

Draw

Solve the system

$$y=-\frac{5}{3}x-6$$

$$y=\frac{1}{6}x+5$$

Multiple Choice

Try Number 2. Solve the system

$$y=5$$

$$y=2x+7$$

• (6, 5)

• (5, 3)

• (-1, 5)

• (5, 17)

Poll

How do you feel about your ability to solve systems of linear equations by graphing?

Awesome. Keep practicing...