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## Solving Systems of Linear Equations by Elimination

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**Solving Systems of Linear Equations by Elimination**Session 6 Practice Test – Sept. 13 LT # 2 – Sept. 15**Objective**• Solve a system of linear equations in two variables by the elimination method.**3x – y = 12 (1)**2x + y = 13 (2) + 5x = 25 x = 5 By what operation can we eliminate a variable in the given system?**3x – y = 12 (1)**2x + y = 13 (2) + 5x = 25 x = 5 (5, 3) 3(5) – y = 12 y = 3 How do we find the value of y?**3x – y = 12 (1)**2x + y = 13 (2) + 5x = 25 x = 5 (5, 3) 3(5) – y = 12 y = 3 How do we know if the values of x and y are correct?**3x – y = 12 (1)**2x + y = 13 (2) (5, 3) 2(5) + 3 = 13 3(5) – 3 = 12 15 – 3 = 12 10 + 3 = 13 13 = 13 12 = 12 (5, 3) How do we know if the values of x and y are correct?**Example 1 page 154**3x + 7y = 17 3x - 6y = 4**Example 2 page 155**4x -5y = 17 x - 5y =8**SYSTEMS THAT HAVE ONLY ONE SOLUTION**(Consistent, Independent) x – 2y = -6 4x + 3y = 20**SYSTEMS THAT HAVE NO SOLUTION**(Inconsistent) y = -1/2x + 2 y = -1/2x + 3**SYSTEMS THAT HAVE NO SOLUTION**(Inconsistent) 2x – 3y = 6 6x – 9y = 36**SYSTEMS THAT HAVE MORE THAN ONE SOLUTION**(Consistent, Dependent) y = -3x + 1 y = -3x + 1**SYSTEMS THAT HAVE MORE THAN ONE SOLUTION**(Consistent, Dependent) 4x + 6y = 4 6x + 9y = 6**For further understanding**• http://www.purplemath.com/modules/systlin5.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**Homework**• Exercise 5c # 2 NSM Book 2 page 163**More Examples on Elimination**3x + 2y = 8 4x - y = 7**More Examples on Elimination**13x - 6y = 20 7x + 4y = 18