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SOLVING SYSTEMS OF EQUATIONS

Learn how to solve systems of equations using graphing as well as elimination. Graphing may not always be the most accurate method, so it's important to explore other options. Follow step-by-step instructions and examples for solving systems of equations using elimination.

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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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