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Published byCameron Stone Modified over 2 years ago

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

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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. SOOOO We need to learn another way!!!!

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

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

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

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Solve: by ELIMINATION 5x - 4y = x + 4y = 18 We need to eliminate (get rid of) a variable. The ys be will the easiest.So, we will add the two equations. 3x = -3 Divide by 3 x = -1 THEN---- Like variables must be lined under each other.

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

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5x - 4y = -21 5(-1) – 4(4) = = = x + 4y = 18 -2(-1) + 4(4) = = = 18

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Solve: by ELIMINATION 2x + 7y = 31 5x - 7y = - 45 We need to eliminate (get rid of) a variable. The ys will be the easiest. So, we will add the two equations. 7x = -14 Divide by 7 x = -2 THEN---- Like variables must be lined under each other.

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

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2x + 7y = 31 2(-2) + 7(5) = = = 31 5x – 7y = (-2) - 7(5) = = =- 45

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Solve: by ELIMINATION x + 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 xs was negative, it would be eliminated when we add. So we will multiply one equation by a – 1. Like variables must be lined under each other.

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

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

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x + y = = = 30 x + 7y = (- 4) = = 6 6 = 6

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Solve: by ELIMINATION x + 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 1 st equation, the xs would be eliminated when we add. So we will multiply the 1st equation by a – 2. Like variables must be lined under each other.

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

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

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x + y = = 4 4 = 4 2x + 3y = 9 2(3) + 3(1) = = 9 9 = 9

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