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**A f r i d i i m r a n 94@yahoo.com**

S O L V IN G S Y ST E M S O F E Q U A T I O N S A f r i d i i m r a n

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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**

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**

Like variables must be lined under each other. Solve: by ELIMINATION x + 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----

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**Now check our answers in both equations------**

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

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

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**Solve: by ELIMINATION 5x - 4y = -21 -2x + 4y = 18**

Like variables must be lined under each other. Solve: by ELIMINATION 5x - 4y = x + 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----

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**Now check our answers in both equations------**

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

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**5x - 4y = -21 5(-1) – 4(4) = -21 -5 - 16 = -21 -21 = -21**

-2(-1) + 4(4) = 18 = 18 18 = 18

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**Solve: by ELIMINATION 2x + 7y = 31 5x - 7y = - 45**

Like variables must be lined under each other. Solve: by ELIMINATION 2x + 7y = 31 5x - 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----

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**Now check our answers in both equations------**

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

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

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**Solve: by ELIMINATION x + y = 30 x + 7y = 6**

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

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**X + Y = 30 X + Y = 30 -X – 7Y = - 6 ( X + 7Y = 6 ) -1 -6Y = 24 - 6 - 6**

Now add the two equations and solve. - 6 - 6 Y = - 4 THEN----

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**Now check our answers in both equations------**

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

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x + y = = = 30 x + 7y = 6 34 + 7(- 4) = 6 = 6 6 = 6

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**Solve: by ELIMINATION x + y = 4 2x + 3y = 9**

Like variables must be lined under each other. 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 1st equation, the x’s would be eliminated when we add. So we will multiply the 1st equation by a – 2.

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**( ) -2 Y = 1 THEN---- X + Y = 4 -2X - 2 Y = - 8 2X + 3Y = 9**

Now add the two equations and solve. THEN----

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**Now check our answers in both equations------**

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

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

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8-2: Solving Systems of Equations using Substitution

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