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MAT1033 ­ Section 8.2b Solving Systems of Equations Using the Addition/Elimination Method THESE SYSTEMS OF EQUATIONS CAN BE SOLVED ALGEBRAICALLY BY USING THE ADDITION METHOD AS FOLLOWS: A. Add the two equations to see if one variable cancels out. B. If not, multiply one or both of the equations by a constant then add to eliminate one of the variables. C. Solve for the remaining variable. D. Substitute the value of this variable into one of the original equations and solve for the other variable. E. Check your solution in both equations. F. Write your answer as: 1. An ordered pair, 2. No solution, or 3. With set notation (infinite solutions). A. SOLVE THE FOLLOWING SYSTEMS OF EQUATIONS USING THE ADDITION METHOD, MULTIPLY ONE EQUATION IF NECESSARY. 1. x+y=1 -x + y = 5 2. 2x + y = -1 3x - y = -9

3.

2x - y = 8 x + 3y = 4

4.

2x + 2y = 4 -x + 2y = 4

5.

3x + 4y = 21 3x - 3y = 4

6.

x+y=5 x + y = -5

YOU TRY: A. 3x + 4y = 10 6x - 4y = 8 B. x - 5y = 5 3x + y = 31 C. x - 2y = -2 -2x + 4y = 4

B. SOLVE, MULTIPLYING BOTH EQUATIONS TO ELIMINATE ONE VARIABLE 1. 5x + 2y = 8 3x - 5y = 11 2. 3x + 2y = 8 4x - 3y = -12

3. 4x + 3y = 1 5x - 4y = 9

4. 2x + 5y = 11 3x + 8y = 16

Of the three methods for solving systems of equations (graphing, substitution, addition/elimination) which method would work best in each of the following problems? Explain your choice!!

1. y = 2x ­ 5 4y + 3x = 13

2. 5x ­ 4y = 15 2x + 5y = 6

3. y =

2 x­5 3 1 y=- x+1 3

4. 2x = 3y + 6 5x ­ 2y = 15

Hw : Page 491 Solve using addition/elimination: 17, 19, 21, 25, 27, 33 And solve the problems on the "Combined Practice" worksheet using the method of your choice.

MAT 1033 8.2 ­ Combined Practice Solving Systems of Equations Solve the following systems of equations using the method of your choice. You may use as many or few of the graphs as you choose.

1. y + 2x = 5 3x ­ 2y = 4

2. y = x - 5 y = -2x + 4

3. 3x - 4y = 12 5x + 4y = -12

4. y = x + 1 2x - 5y = 4

5. y = 4x + 1 2x + 2y = 7

Answers: 1. ( 2,1 ) 2. ( 3, -2 ) 3. ( 0, -3 ) 4. ( -3, 2 ) 5. , 3

1 2

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