# lecture 2 three systems.pdf - Ex Three systems of linear...

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Ex. Three systems of linear equations 1. x ° y = 1 2 x + y = 6 a) Working with equations: eq.2 - 2 ± eq.1 ) 3 y = 4 ; solve for y : y = 4 3 : Substitute y into eq.1: x = y + 1 = 1 + 4 3 = 7 3 : b) Working with the augmented matrix: " 1 ° 1 1 2 1 6 # R 2 ° 2 R 1 ! R 2 °°°°°°°°°°°! " 1 ° 1 1 0 3 4 # , which corresponds to x ° y = 1 3 y = 4 From the second equation: y = 4 3 : From the °rst: x = 1 + y = 1 + 4 3 = 7 3 : The solution is unique.

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2. x + y = 4 3 x + 3 y = 6 a) Working with equations: eq.2 - 3 ± eq.1 ) 0 ± y = ° 6 : It is impossible to °nd y that satis°es this equation ) the system has no solution. b) Working with the augmented matrix: " 1 1 4 3 3 6 # R 2 ° 3 R 1 ! R 2 °°°°°°°°°°°! " 1 ° 1 1 0 0 ° 6 # ; which corresponds to x + y = 4 0 = ° 6 This system has no solution.
3. 4 x ° 2 y = 1 16

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