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Determinants

Question
CBSEENMA12034700
Wired Faculty App

Examine the consistency of the system of equations:
x + 3y = 5
2x + 6y = 8

Solution

The given equations are
x + 3y = 5
2x + 6y = 8
These equations can be written as
                     open square brackets table row 1 cell space space 3 end cell row 2 cell space space 6 end cell end table close square brackets space open square brackets table row straight x row straight y end table close square brackets space equals space open square brackets table row 5 row 8 end table close square brackets
or     AX space equals space straight B space where space straight A space equals space open square brackets table row 1 cell space space 3 end cell row 2 cell space space 6 end cell end table close square brackets comma space space space straight X space equals space open square brackets table row straight x row straight y end table close square brackets comma space space straight B space equals space open square brackets table row cell table row 5 row 8 end table end cell end table close square brackets
                    open vertical bar straight A close vertical bar space equals space open vertical bar table row 1 cell space space 3 end cell row 2 cell space space 6 end cell end table close vertical bar space equals space 6 minus 6 space equals space 0 space space adj space straight A space equals space open square brackets table row 6 cell space space space minus 2 end cell row cell negative 3 end cell cell space space space space space 1 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row cell space space space 6 end cell cell space space space minus 3 end cell row cell negative 2 end cell cell space space space space space space 1 end cell end table close square brackets therefore space space left parenthesis adj space straight A right parenthesis space straight B space equals space open square brackets table row 6 cell space space space minus 3 end cell row cell negative 2 end cell cell space space space space space space 1 space end cell end table close square brackets space open square brackets table row 5 row 8 end table close square brackets space equals space open square brackets table row cell 30 minus 24 end cell row cell negative 10 plus 8 end cell end table close square brackets space equals space open square brackets table row 6 row cell negative 2 end cell end table close square brackets not equal to space straight O
 ∴   solution does not exist and so system of equations is inconsistent.      

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