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SOLVING SYSTEMS OF EQUATIONS

SOLVING SYSTEMS OF EQUATIONS. BY GRAPHING. Y = 2X + 1 Y = -X + 4. (1,3) IS THE SOLUTION.

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SOLVING SYSTEMS OF EQUATIONS

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  1. SOLVING SYSTEMS OF EQUATIONS

  2. BY GRAPHING Y = 2X + 1 Y = -X + 4 (1,3) IS THE SOLUTION

  3. Graphing is not the only way to solve a system of equations. It is not really the best way because it has to be graphed perfectly and some answers are not integers.SOOOOWe need to learn another way!!!!

  4. Like variables must be lined under each other. Solve: by ELIMINATIONx + y = 12-x + 3y = -8 4y = 4 We need to eliminate (get rid of) a variable. The x’s will be the easiest. So, we will add the two equations. Divide by 4 y = 1 THEN----

  5. Substitute your answer into either original equation and solve for the second variable. X +Y = 12 x + 1 = 12 -1 -1 x = 11 (11,1) Answer Now check our answers in both equations------

  6. X + Y =12 11 + 1 = 12 12 = 12 -x + 3y = -8 -11 + 3(1) = -8 -11 + 3 = -8 -8 = -8

  7. Like variables must be lined under each other. Solve: by ELIMINATION5x - 4y = -21-2x + 4y = 18 3x = -3 We need to eliminate (get rid of) a variable. The y’s be will the easiest.So, we will add the two equations. Divide by 3 x = -1 THEN----

  8. Substitute your answer into either original equation and solve for the second variable. 5X - 4Y = -21 5(-1) – 4y = -21 -5 – 4y = -21 5 5 -4y = -16 y = 4 (-1, 4) Answer Now check our answers in both equations------

  9. 5x - 4y = -215(-1) – 4(4) = -21-5 - 16 = -21-21 = -21 -2x + 4y = 18 -2(-1) + 4(4) = 18 2 + 16 = 18 18 = 18

  10. Like variables must be lined under each other. Solve: by ELIMINATION2x + 7y = 315x - 7y = - 45 7x = -14 We need to eliminate (get rid of) a variable. The y’s will be the easiest. So, we will add the two equations. Divide by 7 x = -2 THEN----

  11. Substitute your answer into either original equation and solve for the second variable. 2X + 7Y = 31 2(-2) + 7y = 31 -4 + 7y = 31 4 4 7y = 35 y = 5 (-2, 5) Answer Now check our answers in both equations------

  12. 2x + 7y = 312(-2) + 7(5) = 31-4 + 35 = 3131 = 31 5x – 7y = - 45 5(-2) - 7(5) = - 45 -10 - 35 = - 45 - 45 =- 45

  13. Like variables must be lined under each other. Solve: by ELIMINATIONx + y = 30 x + 7y = 6 We need to eliminate (get rid of) a variable. To simply add this time will not eliminate a variable. If one of the x’s was negative, it would be eliminated when we add. So we will multiply one equation by a – 1.

  14. X + Y = 30 X + Y = 30 -X – 7Y = - 6 ( X + 7Y = 6 ) -1 -6Y = 24 Now add the two equations and solve. - 6 - 6 Y = - 4 THEN----

  15. Substitute your answer into either original equation and solve for the second variable. X + Y = 30 X + - 4 = 30 4 4 X = 34 (34, - 4) Answer Now check our answers in both equations------

  16. x + y = 3034 + - 4 = 3030 = 30 x + 7y = 6 34 + 7(- 4) = 6 34 - 28 = 6 6 = 6

  17. Like variables must be lined under each other. Solve: by ELIMINATIONx + y = 4 2x + 3y = 9 We need to eliminate (get rid of) a variable. To simply add this time will not eliminate a variable. If there was a –2x in the 1st equation, the x’s would be eliminated when we add. So we will multiply the 1st equation by a – 2.

  18. ( X + Y = 4 ) -2 -2X - 2 Y = - 8 2X + 3Y = 9 2X + 3Y = 9 Y = 1 Now add the two equations and solve. THEN----

  19. Substitute your answer into either original equation and solve for the second variable. X + Y = 4 X + 1 = 4 - 1 -1 X = 3 (3,1) Answer Now check our answers in both equations------

  20. x + y = 43 + 1 = 4 4 = 4 2x + 3y = 9 2(3) + 3(1) = 9 6 + 3 = 9 9 = 9

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