Section 7.3 Solving Systems By Linear Combination

Section 7.3 Solving Systems by Linear Combination

ALGEBRA B

Linear Combination (AKA Elimination) 1. Move x’s and y’s to the left side of equations 2. Get a pair of opposite coefficients on the same variable 3. Add the equations 

One variable should cancel

4. Solve for one variable 5. Substitute value from step 5 into one of the original equations 6. Solve for other variable 7. Check your solution!

Examples: Solve by linear combination

1.

x 2y

8

x 6y

8y y

16

x 2( 3) x 6

8 8

24 3

x x

2 2

(2, 3)

Examples: Solve by linear combination

2. 9 x 6 y 18 12 x 6 y

3x

9( 2) 6 y 18

12

18 6 y 18

6

x

6 y 36 y 6

2 ( 2,6)

Assignment  P.405

#15-22 all (8 problems)

3. 2( 5 x 4 y 2x 8 y 10 x 8 y 2x 8 y

33) 2

1 5 3

5 4y 3

6 2

12x 4 4 x 12 1 x 3

4y

1 1 , 3 3

3

3

4y

4 3

y

1 3

Examples: Solve by linear combination

4. 5(77 x 12 12 y 7( 55 x 88 y

22) 22 14) 14

35 x 60 y

110

35 x

56 y

98

4y

12

y

3

7 x 12(3)

22

7 x 36 22 7 x 14 x

(2,3)

2

Examples: Solve by linear combination

5. 3 x

6 y 12

x 3y 6 3x 6 y 12 3( x 33 y 6) 6 3 x 6 y 12 3 x 9 y 18

15 y 30 y

2

3x

3x

6(2) 12

12 12 3x 0 x 0

(0,2)

Examples: Solve by linear combination

6. 7 y 12 x 3x

7 y 12 5

5 y 10

7y 7

12 5( x 77 y 12) 10 7(33 x 55 y 10) 5 x 35 y 60 21 x 35 y 70

26 x

130

x 5

y 1

(5,1)

Assignment  P.405

#31-42 all (12 problems)