Question

$If space 2 straight X plus 3 straight Y equals space open square brackets table row 2 3 row 4 0 end table close square brackets space and space 3 straight X plus 2 straight Y equals open square brackets table row cell negative 2 end cell 3 row 1 cell negative 5 end cell end table close square brackets$ .find X and Y.

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Solution

2 straight X plus 3 straight Y equals space open square brackets table row 2 3 row 4 0 end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis 3 straight X plus 2 straight Y equals open square brackets table row cell negative 2 end cell 3 row 1 cell negative 5 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis

Multiplying (I) by 2 and (2) by 3, we get,

4 straight X plus 6 straight Y equals open square brackets table row 4 6 row 8 0 end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 3 right parenthesis 9 straight X plus 6 straight Y equals open square brackets table row cell negative 6 end cell 6 row 3 cell negative 15 end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space... left parenthesis 4 right parenthesis

Subtracting (3) from (4), we get,

5 straight x equals open square brackets table row cell negative 6 minus 4 end cell cell 6 minus 6 end cell row cell 3 minus 8 end cell cell negative 15 minus 6 end cell end table close square brackets therefore space space space 5 straight x equals open square brackets table row cell negative 10 end cell 0 row cell negative 5 end cell cell negative 15 end cell end table close square brackets space rightwards double arrow space straight X equals 1 third open square brackets table row cell negative 10 end cell 0 row cell negative 5 end cell cell negative 15 end cell end table close square brackets therefore space space space straight x equals open square brackets table row cell negative 2 end cell 0 row cell negative 1 end cell cell negative 3 end cell end table close square brackets therefore space from left parenthesis 1 right parenthesis comma space open square brackets table row cell negative 4 end cell 0 row cell negative 2 end cell cell negative 6 end cell end table close square brackets plus 3 straight Y equals open square brackets table row 2 3 row 4 0 end table close square brackets therefore space space space 3 straight Y equals open square brackets table row 2 3 row 4 0 end table close square brackets minus open square brackets table row cell negative 4 end cell 0 row cell negative 2 end cell cell negative 6 end cell end table close square brackets space space rightwards double arrow space 3 straight Y equals open square brackets table row cell 2 plus 4 end cell cell space space space space space 3 minus 0 end cell row cell 4 plus 2 end cell cell space space space space space space 0 plus 6 end cell end table close square brackets rightwards double arrow space space space 3 straight Y equals open square brackets table row 6 3 row 6 6 end table close square brackets space space space rightwards double arrow straight y equals 1 third open square brackets table row 6 3 row 6 6 end table close square brackets equals open square brackets table row 2 1 row 2 2 end table close square brackets therefore space space straight X equals open square brackets table row cell negative 2 end cell 0 row cell negative 1 end cell cell negative 3 end cell end table close square brackets comma space straight Y equals open square brackets table row 2 1 row 2 2 end table close square brackets

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