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Mastering Systems of Equations Through Graphing: Homework Review

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This homework review focuses on understanding and solving systems of equations by graphing. Students will learn to draw a coordinate plane, graph given equations, and find points of intersection between two lines. Key concepts include identifying parallel, intersecting, and coincidental lines, and understanding the implications of each type on the number of solutions. The review also features hands-on activities to visualize the intersection of lines and employs technology for checking work, enhancing the problem-solving process in Algebra I.

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Mastering Systems of Equations Through Graphing: Homework Review

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  1. Homework Review… • Draw a coordinate plane. • Graph the following equations… (on the same graph) • Find the point of intersection of the two lines.

  2. Homework Review… • Intersection – the place or point where two or more things come together or cross • System – a group of related parts that move or work together

  3. Homework Review…

  4. Unit 7Systemsof Equations & Inequalities Algebra I

  5. Solve systems of equations by GRAPHING Algebra I ~ Unit 7

  6. Objectives • I will be able to solve a system of equations by graphing. • I will be able to identify the number of solutions a system of equation has by graphing.

  7. System of Equations • A system of equationsis a set of at least two equations in the same variables that are considered (or solved) together. • To solve a system of equations, you must find a solution that will make both equations true. • Systems can be solved either… • Graphically • Algebraically

  8. Explore • How many ways can straight lines cross? Try using your arms. Your left arm as one linear equation, and the right arm as the other linear equation. How many ways can you get them to cross?

  9. Two linear equations can be… • Never touching Parallel Lines same slope, dif. y-int. No Solution • Only cross at one point Intersecting Lines dif. slope, dif. y-int. One Solution • Lying on top of one another Coincidental Lines same slope, same y-int. Infinite Solutions

  10. Given the system of equations, determine if they are parallel, intersecting, or coincidental. How many common solutions do the equations have? Graph the two equations. Ex.1 and

  11. Given the system of equations, determine if they are parallel, intersecting, or coincidental. How many common solutions do the equations have? Graph the two equations. Ex.2 and

  12. Given the system of equations, determine if they are parallel, intersecting, or coincidental. How many common solutions do the equations have? Graph the two equations. Ex.3 and

  13. The graph below shows a system of equations. What are the two equations, and what is the solution of the system? Ex.4 1st slope 2nd y-intercept 3rd equations 4th intersection

  14. Groups • Find the solution of each system by graphing. • AChange first equation to slope-intercept form. • BChange second equation to slope-intercept form. • CGraph the two equations. • DWrite out the solution and what that means.

  15. Check your work - Calculator • Put your equations in [y=]Y1= Y2= • Press [2nd] [Calc] or [Trace] [5] [enter] [enter] [enter]

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