Solving System of Equations by Graphing

System of Equations

Graphing Method

Learning Target

1. I know what system of equations are

2. I know the 3 types of solutions

3. I can correctly perform the graphing method

4. I know what type of lines make what type of solution.

Multiple Choice

• Positional point

• Number

• Ordered pair

• Graphing term

Multiple Choice

"y=mx+b", where m is the slope and b is the y-intercept of the line

• Slope - Intercept Form

• Point - Slope Form

• Standard Form

Vocabulary

A system of equations consists of two or more equations with the
same variables. For example, the linear equations below create a
system of linear equations:

y=2x–8
3x–4y=7

A solution to a system of equations is a set of values that makes
each equation in the system true. The solution to the system of
equations above can be written as the ordered pair (5,2) because
x=5 and y=2 satisfy both equations in the system.

Vocabulary

Systems of two linear equations that have no solution
are called inconsistent.

Systems of two linear equations that have at least
one solution are called consistent.

Consistent systems of two linear equations that have
exactly one solution are called independent.

Consistent systems of two linear equations that have
an infinite number of solutions are called dependent

Fill in the Blank

A system of linear equaations is a set of ______ or more linear equations.

Multiple Choice

• Consistent System

• Independent System

• Inconsistent System

• System of Substitutions

Multiple Choice

• Cystic System

• Similar System

• Dependent System

• Independent System

What type of lines?

Intersecting Lines

What do you NOTICE
about the equations?

What is the type
of SOLUTION?

What type of Lines?

Parallel Lines

What do you NOTICE about the equations?

What is the type
of SOLUTION?

What type of Lines?

Coinciding or Same
Line

What do you NOTICE
about the equations?

What is the type of
Solution?

Multiple Choice

• Dependent System

• Inconsistent System

• Consistent System

• Irregular System

Multiple Choice

When you graph the exact same equation twice,

• you will have no solution. 
• you will have one solution.
• you will have infinite solutions. 
• you will graph a giraffe. 

Multiple Choice

What is the solution to this system?

• (1, -1)
• (-1, 1)
• (0, -2)
• (2, 0)

Steps to Graphing Method

1. Make sure BOTH equations are in Slope-Intercept

Form. Y=MX+B

2. Graph each equation starting from the Y-intercept.

Use the slope to make additional points.

3. Determine the type of lines created on the graph

4. Determine the SOLUTION

5. if it is one solution, state the solution as an ordered

pair. Ex. (5,7) Do not Abbreviate the WORDS.

Solve using the graphing method

Step 1:Make sure that each equation is in Slope Intercept Form. Y=MX+B. Remember that M=slope and B=Y-intercept.

Step 2: Graph each equation starting from the Y-intercept.
Use the slope to make additional points.

y-intercept=8

Slope= down 3 and right 8

y-intercept=3

Slope= Up 1 & Right 4

Step 3: Determine the type of lines created on the graph

These are intersecting Lines

Step 4 : Determine the SOLUTION

Intersecting Lines
have One Solution

When it is one
solution write your
answer as an
ordered pair. (x,y)
(8,5)

Multiple Choice

What is the solution to the system?

• (3, -1)
• (2, -6)
• No Solution 
• (6, -2)