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Mastering Line Intersections and Systems of Equations: Elimination and Graphing Techniques

In this lesson, we build upon last week's knowledge of line equations and their graphical representations. We'll delve into finding the intersection of two lines, using substitution and elimination methods. We’ll examine example equations to determine slope-intercept forms, graph the lines, and identify common points of intersection. Prepare for our upcoming quiz by practicing graphing equations and understanding the relationships between parallel and perpendicular lines. Be ready to tackle problems in your notebook focusing on systems of equations and elimination techniques.

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Mastering Line Intersections and Systems of Equations: Elimination and Graphing Techniques

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  1. BELL RINGER • G1/G2: Be ready to show problem #27 • G3/G4: Be ready to show problem #29 • G5/G6: Be ready to show problem #31

  2. Summary • Last week, we learned: • Finding the equation of any line using point-slope, slope intercept, or standard form • Graphing using intercepts • Determining parallel & perpendicular lines through any point • Finding the intersection of two lines using ‘substitution’ or by graphing.

  3. Line Intersections & Systems of Equations • First, let’s observe the two equations: • 2x + y = 8 & x – y = 10. • Determine the slope-int forms, graph, and find intersection. • (6, -4) is common point between BOTH lines, and the solution to the system.

  4. New Method - Elimination 2x + y = 8 x – y = 10 (ADD them together) __________ 3x + 0 = 18 3x = 18 x = 6  6 – y = 10  y = -4. (6, -4) point of intersection and solution.

  5. Elimination Examples 2x + 5y = 15 -4x + 7y = -13 Does adding these together help our cause? What if . . . 2(2x + 5y) = 2(15) 4x + 10y = 30 Now Let’s Try Again . . .

  6. -cnt’d- 4x + 10y = 30 -4x + 7y =-13 ____________ Add Together . . . 17y = 17  y = 1 4x + 10(1) = 30, 4x = 20  x = 5 (5, 1) point of intersection

  7. QUIZ TOMORROW! • P. 169, #9-12 (practice elimination) • Be able to graph, given an equation in any form, or any info/data. • Find the equation of any specific line in any form given any set of criteria. • Know parallel/perpendicular slope’s relationships • Find the intersection of two lines using substitution or elimination. • Notebook: linequ1, linequ2, linequ3, systems, elim

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