Math, asked by harshpancholi, 4 hours ago

solve by elimination method
4y+6x=18
3y-2x=33

Answers

Answered by ajay8949
0

 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \sf{6x + 4y = 18}

 \:  \:  \:  \:  \:  \sf{multiply \: both \: sides \: by \: 2}

⇢  \:  \:  \:  \: \sf{2(6x + 4y) = 2(18)}

⇢ \: \:  \:  \:  \:  \:  \:  \:  \sf {12x + 8y = 36} \: -  (i)

 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \sf{ - 2x + 3y = 33}

 \:  \:  \:  \:  \:  \:  \sf{multiply \: both \: sides \: by \:  - 6}

⇢  \:  \: \sf{ - 6( - 2x + 3y) = - 6 (33)}

⇢ \:  \:  \:  \:  \:  \sf{12x - 18y =  - 198} \: - ( ii)

 \sf{now \: eliminating\: eq {}^{n}  \: 1 \: from \: eq {}^{n} 2}

 \sf{ (12x - 18y) - (12x + 8y) =  - 198 - 36}

  \:  \:  \: \sf { \cancel{12x} - 18 y \:  \cancel{ - 12x} - 8y =  - 234}

⇢ \:  \:  \:  \:  \:  \:  \:  \sf{ -2 6 y =  - 234}

⇢ \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \fcolorbox{pink}{aqua}  {\sf{ y = 9 \: }}

  \:  \:  \:  \: \sf{substituting \: value \: of \: y \: in \: eq {}^{n}1  \: }

⇢ \:  \:  \:  \:  \:  \:  \:  \sf{12x + 8(9) = 36}

⇢  \:  \:  \:  \:  \:  \:  \:  \:  \sf{12x + 72 = 36}

⇢ \:  \:  \:  \:  \:  \:  \:  \:  \:  \sf { 12x = -  36}

⇢  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \fcolorbox{pink}{yellow} {\sf{x =  - 3}}

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