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Systems of Equations Sasha Merkel ITC 525 Summer Session I 2010 Contact Me

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Are you ready for systems of equations? Solving Graphically Additional Resources Standards Addressed Credits

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Review Types of Solutions What are systems of equations?

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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.

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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,

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One Solution Many Solutions No Solution

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Directions Examples Ex. 1 Ans.Ex. 2 Ans.Ex. 3 Ans. Practice

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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.

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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.

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One Solution 2y + x = 8 y = 2x + 4 Ex. 1

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No Solution x - 5y = 10 -5y = -x +6 Ex. 2

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Many Solutions Ex. 3 y = -6x + 8 y + 6x = 8

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Practice 3 Practice 1 Practice 2

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One Solution Practice 1 No Solution Many Solutions

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Practice 2 One Solution No Solution Many Solutions y = x - 1 y = 3 23

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Practice 3 One Solution No Solution Many Solutions x + 2y = 6 x + 2y = 8

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the two lines will only intersect at one point One Solution: TRY AGAIN!

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No Solution: when lines of a graph are parallel when lines of a graph are parallel since they do not intersect, there is no solution since they do not intersect, there is no solution TRY AGAIN!

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

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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!

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6. Technology Operations and Concepts Students 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 Equations Anchor 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)

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"Free Algebra 2 Worksheets." Create Custom Pre-Algebra, Algebra 1, Algebra 2, and Geometry Worksheets. Kuta Software. Web. 05 June 2010.. 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.. "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.. Keeler, Alice. "Systems of Equations Jeopardy." Quia. Quia. Web. 04 June 2010.. Quit

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EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 2x – 3y = 18.

EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 2x – 3y = 18.

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