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Consider the following system of equations . y = 2x - 4 y = -x - 5

Write down this problem on your READY RECALL SHEET Be prepared to explain your answer if you are called on. Consider the following system of equations . y = 2x - 4 y = -x - 5 Identify the slope and y-intercept of the graph of each equation .

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Consider the following system of equations . y = 2x - 4 y = -x - 5

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  1. Write down this problem on your READY RECALL SHEET Be prepared to explain your answer if you are called on. Consider the following system of equations. y = 2x - 4 y = -x - 5 Identify the slope and y-intercept of the graph of each equation. b. Based on your answer for part (a), are the graphs of the two lines intersecting lines, the same line, or parallel lines? Explain. i-can find the solution by using the Elimination method: -4x - 15y = -17 -x + 5y = -13 Page 92 of your INB

  2. ITEMS of BUSINESS

  3. Questions on Homework? then Trade-n-Grade

  4. SYSTEMS OF EQUATIONS 11.3 Solving Systems by Elimination

  5. Get into your Groups i-can find the solution by using the Elimination Method: -4x - 15y = -17 -x + 5y = -13 Page 92-93 of your INB

  6. MATHICAL MAGGIE Did you know I’m Magic? I can read your mind Think of 2 numbers Tell me the Sum and Difference

  7. MATHICAL MATT/MAGGIE ARE YOU MAGICAL NOW? Show your Partner Think of 2 numbers Tell them the Sum and Difference

  8. How is it done Algebraically? For any x or y = x x + y = SUM x – y= DIFFERENCE SUM – x =y Ex. x + y = 30 x – y = 6 x = 18 y = 12 30 – 18 = 12 = 18 I’M USING THE ELIMINATION METHOD!! x + y = 30 x – y = 6 ADD THE TWO EQUATIONS TOGETHER & SOLVE 18 + y = 30 REPLACE x WITH 18 IN ONE OF THE ORIGINAL EQUATIONS & SOLVE FOR Y y = 30 - 18 2x = 36 y = 12 2 2 x = 18 x = 18,y = 12 (18,12)

  9. Open your Books to page 648 .

  10. ELIMINATION METHOD PG. 648

  11. ELIMINATION METHOD PG. 648

  12. ELIMINATION METHOD PG. 649 x = 179 girls; y = 145 boys

  13. LETS TRY A PROBLEM  Front Page of your homework: A. Guided Practice 1. x- y = 11 2x + y = 19

  14. IS THIS TRUE? y = 4 If we have… Multiply each side by 3, will it still be true? Multiply each side by 2, will it still be true? 3(y) = 3(4) 2(y) = 2(4) 3y = 12 2y = 8 y = 4 y = 4 Sooo… Is each equation still true if we Multiply each side with a Scaler orOppositizethem? Multiply each side by -1, or oppositizeboth sides. Will it still be true? -1(y) = -1(4) -1y = -4 y = 4

  15. LETS PRACTICE WITH OUR COMMUNICATORS Example: Multiply both sides with 3 x + 2y = 7 3x + 6y = 21 A. Multiply both sides with 2 3x - y = 4 6x - 2y = 8 B. Multiply both sides with -4 x - 4y = 2 -4x + 16y = -8 C. Oppositize both sides x - 3y = -5 -x + 3y = 5

  16. What would you do to prepare these equations for elimination? B.

  17. ELIMINATION When using Elimination, we might need to use a Scaler or to Oppositize in order to eliminate a variable. Front Page of your homework: A. Guided Practice 2. 7x+ 2y = 24 8x + 2y = 30

  18. { 5x + 2y = 12 A. Solve by Elimination: -5x + 4y = -66 + 6y = -54 6 6 y = -9 INB NOTEBOOK ACTIVITY 5x + 2y = 12 5x + 2(-9) = 12 5x - 18 = 12 +18 +18 5x = 30 Solution: (6, -9) x, y 5 5 x = 6

  19. B. Solve by Elimination: { ()3 3x – 5y = -6-9x + 15y = 13 9x – 15y = -18 + INB NOTEBOOK ACTIVITY -9x + 15y = 13 0 = -5 Is this true? No! NO SOLUTION

  20. { C. Solve by Elimination: ()3 ()2 2x – 4y = 6 -3x + 6y = -9 6x – 12y = 18 + INB NOTEBOOK ACTIVITY -6x + 12y = -18 0 = 0 Is this true? Yes! Infinite Solutions

  21. POSSIBLE SOLUTIONS FOR 2 EQUATIONS (1,3) Infinitely Many Solutions One Solution No Solution Parallel Lines Same slope, different y-int. Coincidental Lines Same line, same slope, same y-int. Intersecting Lines Same Slope, y-int. can be different or the same Solve Algebraically: Variables drop out TRUE Statement ex. 22 = 22 Solve Algebraically: Variables drop out FALSE Statement ex. 12 = 9 Solve Algebraically: You will get one solution (X,Y)

  22. INB NOTEBOOK ACTIVITY ONE SOLUTION: (X,Y) ONE SOLUTION: (X,Y) FALSE STATEMENT FALSE STATEMENT TRUE STATEMENT TRUE STATEMENT

  23. LETS TRY A FEW PROBLEMS Second Page of your homework: B. Guided Practice 2. 2x – y = 3 4x - 2y = 6 1. 2x - y = 5 2x – y = 7

  24. 11.3 Solving Systems by Elimination i-can find the solution by using the Elimination method: -4x - 15y = -17 -x + 5y = -13 Number 14 on your Homework

  25. Write down today’s homework on your CALENDAR CARD. BLUE Worksheet 11.3 Solving Systems by Elimination  SHOW YOUR WORK

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