Solving Systems of Linear Equations by Elimination

Session 6

Practice Test – Sept. 13

LT # 2 – Sept. 15

ObjectiveSolve a system of linear

equations in two variables by the elimination method.

3x – y = 12 (1)2x + y = 13 (2)

By what operation can we eliminate a variable in the given system?

+

5x = 25

x = 5

3x – y = 12 (1)2x + y = 13 (2)

How do we find the value of y?

+

5x = 25

x = 5

3(5) – y = 12

y = 3

(5, 3)

3x – y = 12 (1)2x + y = 13 (2)

How do we know if the values of x and y are correct?

+

5x = 25

x = 5

3(5) – y = 12

y = 3

(5, 3)

3x – y = 12 (1)2x + y = 13 (2)

How do we know if the values of x and y are correct?

(5, 3)

3(5) – 3 = 12

15 – 3 = 12

12 = 12

2(5) + 3 = 13

10 + 3 = 13

13 = 13

(5, 3)

3x + 7y = 173x - 6y = 4

Example 1 page 154

4x - 5y = 17x - 5y = 8

Example 2 page 155

SYSTEMS THAT HAVE ONLY ONE SOLUTION(Consistent, Independent)

x – 2y = -6 4x + 3y = 20

SYSTEMS THAT HAVE NO SOLUTION(Inconsistent)

y = -1/2x + 2y = -1/2x + 3

SYSTEMS THAT HAVE NO SOLUTION(Inconsistent)

2x – 3y = 66x – 9y = 36

y = -3x + 1y = -3x + 1

SYSTEMS THAT HAVE MORE THAN ONE SOLUTION(Consistent, Dependent)

4x + 6y = 46x + 9y = 6

SYSTEMS THAT HAVE MORE THAN ONE SOLUTION(Consistent, Dependent)

For further understanding http://www.purplemath.com/modules/sy

stlin5.htm

http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut19_systwo.htm#elimination

http://www.regentsprep.org/Regents/math/ALGEBRA/AE3/AlgSysAdd.htm

http://www.youtube.com/watch?v=6c7OPYQLVG0&feature=relmfu

HomeworkExercise 5c # 2

NSM Book 2 page 163

3x + 2y = 84x - y = 7

More Examples on Elimination

13x - 6y = 207x + 4y = 18

More Examples on Elimination

More Examples on Elimination