Systems of Equations

Sasha Merkel ITC 525Summer Session I2010

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Are you ready for

systems of equations?

Solving Graphically

Additional Resources

Standards Addressed

Credits

Review

Types of Solutions

What are systems

of equations?

Before we begin, we need to review some basic math skills that we have

already acquired.

Select the icon to begin the 4 question review. All answers will be submitted to me via email.

You can check your answer after completing the review.

A system of equations is a set of equations that you deal with all together at once. It is impossible to solve a system of equations only using one of the equations, because you have more than one variable.

The variables represent the same number in all of the equations,

One Solution Many Solutions

No Solution

Directions

ExamplesEx. 1 Ans.

Ex. 2 Ans.

Ex. 3 Ans.Practice

There are 4 steps to solving a linear system using a graph.

Step 1: Put both equations in slope - intercept form.

Solve both equations for y, so that each equation looks like y = mx + b.

Step 2: Graph both equations on the same coordinate plane.

Step 3: Estimate where the graphs intersect.

Step 4: Check to make sure your solution makes both equations true.

Use the slope and y - intercept for each equation in step 1. Be sure to use a ruler and graph paper!

This is the solution! LABEL the solution!

Substitute the x and y values into both equations to verify the point is a solution to both equations.

Ex. 3

Ex. 1

Ex. 2

2y + x = 8

y = 2x + 4

x - 5y = 10

-5y = -x +6

y = -6x + 8

y + 6x = 8

Click on the question mark

below to receive the step by step

directions on how to solve again.

One Solution

2y + x = 8

y = 2x + 4Ex. 1

No Solution

x - 5y = 10

-5y = -x +6Ex. 2

Many Solutions

Ex. 3y = -6x + 8

y + 6x = 8

Practice 3

Practice 1

Practice 2

One Solution

Practice 1

No Solution

Many Solutions

2

3x

1

4y+ 4=

1

3x

1

8y+ 2=

Practice 2

One Solution

No Solution

Many Solutions

y = x - 1

y = 3

23

Practice 3

One Solution

No Solution

Many Solutions

x + 2y = 6

x + 2y = 8

• the two lines will only intersect at one point

One Solution:

TRY AGAIN!

No Solution: • when lines of a graph are parallel

• since they do not intersect, there is no solution

TRY AGAIN!

Many Solutions: • a pair of equations that have the same slope and y-intercept.

TRY AGAIN!

Click here for directions on how to solve linear system on your graphing calculator!

Still struggling? Try watching this video!

Need more practice? Download this worksheet to help you master system of equations.

Play Systems of Equations Jeopardy online!

Interactive System of Linear Equations. Drag around the points on the lines and watch this interactive system and its solution in action!

6. Technology Operations and ConceptsStudents demonstrate a sound understanding of

technology concepts, systems, and operations. Students:a. understand and use technology systems.b. select and use applications effectively and

productively.

Assessment Anchor – A1.1.2:Linear EquationsAnchor Descriptor –

A1.1.2.2: Write, solve and/or graph systems of linear equations using various methods.

Eligible Content – A1.1.2.2.1: Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or

elimination (limit systems to 2 linear equations). A1.1.2.2.2: Interpret solutions to problems in the context of the

problem situation (systems of 2 linear equations only).

(ALGEBRA I)

"Free Algebra 2 Worksheets." Create Custom Pre-Algebra, Algebra 1, Algebra 2, and Geometry Worksheets. Kuta Software. Web. 05 June 2010.

<http://www.kutasoftware.com/freeia2.html>. Harland, Julie. "Solving Systems of Equations by Graphing Pt 2 Help Video in High School Math Algebra -- Free Math Help Videos Online by MathVids.com." Free Math Help and Free Math Videos Online at MathVids.com. Math Vids, 20 Nov. 2009. Web. 04 June 2010. <http://www.mathvids.com/lesson/mathhelp/967-solving-systems-of-equations-by-graphing-pt-2>."Interactive System of Linear Equations. Drag around the Points on the Lines and Watch This Interactive System and Its Solution in Action..." Interactive Math Activities, Demonstrations, Lessons with Definitions and Examples, Worksheets, Interactive Activities and Other Resources. Math Warehouse. Web. 05 June 2010. <http://www.mathwarehouse.com/algebra/linear_equation/systems-of-equation/interactive-system-of-linear-equations.php>.Keeler, Alice. "Systems of Equations Jeopardy." Quia. Quia. Web. 04 June 2010. <http://www.quia.com/cb/79607.html>.

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