SQC63.pdf - Linear equations II Linear Equations is one of...

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Session Algebra Linear equations – II Linear Equations is one of the most important topics for CAT and other aptitude exams, questions from which have consistently appeared in all these exams. Key concepts discussed: A system of equations 1 1 1 2 2 2 a x b y c 0 and a x b y c 0 + + = + + = has a unique solution if and only if 1 1 2 2 a b a b . A system of equations 1 1 1 2 2 2 a x b y c 0 and a x b y c 0 + + = + + = has infinite solutions if and only if 1 1 1 2 2 2 a b c a b c = = . A systems of equations 1 1 1 2 2 2 a x b y c 0 and a x b y c 0 + + = + + = has no solution if and only if 1 1 1 2 2 2 a b c . a b c = If 1 1 1 1 2 2 2 2 a x b y c z d and a x b y c z d + + = + + = are given and the value of 3 3 3 a x b y c z + + is asked, then following are the steps that may be followed in order to calculate the required value: o Let 3 1 2 a a ka = + ; 3 1 2 b b kb = + ; 3 1 2 c c kc . = + Using any of the three equations find the value of K. o Multiply the first equation by 1 and the second by the obtained value of k and then add the two resultant equations. The figure on right hand side of the final equation will be the required answer.
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