A 3x y 4 b x 4y 5 x y 8 x 2y 7 c 2x y 3 d 2x 3y 1 4x

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a) 3x – y = 4 b) x + 4y = 5 x + y = 8 x + 2y = 7 c) 2x + y = 3 d) 2x + 3y = –1 4x – 3y = 1 x + y = 3 Solutions: 1.a) (3,5) b) (9,-1) c) (1,1) d) (10,-7) 2. a) (1,1) b) (2,-1) 3 - 6
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3 4 3 6 5 3 y x y x 2 4 19 3 y x y x MFM 2P Date: ________________________ Unit 3: Linear Systems 3.3 Solving Linear Systems by Elimination If the coefficients of the same VARIABLE in both equations have the same COEFFICIENT, you can eliminate that variable by ADDING or SUBTRACTING the equations. This is called the process of ELIMINATION . Example 1. Solve the linear system by elimination . Then perform a LS=RS Check to verify your solution. In this example, the variable X has the same coefficient in both equations. 1. We can SUBTRACT in order to eliminate the x. 2. Remember, whatever you do to one term you must do to all terms ! 3. So we must also subtract the Y terms and the constants (term without a variable). 4. We are left with 1 variable,Y , which we can easily solve for! Let’s solve for y. 5. Now replace your answer for y in one of the equations to find x . CHECK: LS = RS = CHECK: LS = RS = Solution: ____________ Example 2. Solve the linear system by elimination . Then perform a LS=RS Check to verify your solution. In this example, the variable Y has the same coefficient in both equations. 1. We can ADD in order to eliminate the y. 2. Remember, whatever you do to one term you must do to all terms ! So we must also add the X terms and the constants (term without a variable). 3. We are left with 1 variable, X , which we can easily solve for! Let’s solve for x. 4. Now replace your answer for x in one of the equations to find y . CHECK: LS = RS = CHECK: LS = RS = Solution: ____________ 3 - 7
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MFM 2P Date: ________________________ Unit 3: Linear Systems 3.3 Solving Linear Systems by Elimination Practice 2. Solve for the linear systems in question 1, using the appropriate operation. a) b) d) e) f) 3 - 8
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MFM 2P Date: ________________________ Unit 3: Linear Systems Solutions: 1.a) x by subtraction b) x by subtraction c) y by subtraction d) y by addition e) y by subtraction f) x by subtraction or y by addition 2.a) (3,1) b) (2,-1) c) (-1,3) d) (1,0) e) (0,-2) f) (3,1) 3.a) (-1, 1) b) (2, 3) 3 - 9
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MFM 2P Date: ________________________ Unit 3: Linear Systems 3.4 Solving Linear Systems Using Elimination continued Yesterday, we learned a new method of solving a linear system: by ______________________. Today, we will continue to explore more examples. Example 1. Solve the following linear system using elimination 6 2 4 y x What do you notice? 6 y x So…what can we do??? We MULTIPLY ALL TERMS in the equation by the SAME COEFFICIENT number so that the COEFFICIENTS of one of the variables have the SAME VALUE 1. Choose a variable. ________ 2. How can you change the equation so that they have the same coefficient ? Multiply each term by ________ 3. Now _________________ the equations to eliminate the ______.
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