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Jawaban:

Untuk dapat menentukan pertidaksamaan linear dua variabel maka perlu menentukan persamaan garis pembatasnya.

Garis I melalui titik begin mathsize 14px style open parentheses 0 comma space 40 close parentheses end style dan begin mathsize 14px style open parentheses 20 comma space 0 close parentheses end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator y minus y subscript 1 over denominator y subscript 2 minus y subscript 1 end fraction end cell equals cell fraction numerator x minus x subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction end cell row cell fraction numerator y minus 40 over denominator 0 minus 40 end fraction end cell equals cell fraction numerator x minus 0 over denominator 20 minus 0 end fraction end cell row cell fraction numerator y minus 40 over denominator negative 40 end fraction end cell equals cell x over 20 end cell row cell 20 y minus 800 end cell equals cell negative 40 x end cell row cell 40 x plus 20 y end cell equals 800 row cell 2 x plus y end cell equals 40 row blank blank blank end table end style 

Garis II melalui titik begin mathsize 14px style open parentheses 0 comma space 30 close parentheses end style dan begin mathsize 14px style open parentheses 40 comma space 0 close parentheses end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator y minus y subscript 1 over denominator y subscript 2 minus y subscript 1 end fraction end cell equals cell fraction numerator x minus x subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction end cell row cell fraction numerator y minus 30 over denominator 0 minus 30 end fraction end cell equals cell fraction numerator x minus 0 over denominator 40 minus 0 end fraction end cell row cell fraction numerator y minus 30 over denominator negative 30 end fraction end cell equals cell x over 40 end cell row cell 40 y minus 1200 end cell equals cell negative 30 x end cell row cell 30 x plus 40 y end cell equals 1200 row cell 3 x plus 4 y end cell equals 120 end table end style 

Perhatikan daerah penyelesaian pada soal, sehingga diperoleh sistem pertidaksamaan linear dua variabel yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus y end cell greater or equal than 40 row cell 3 x plus 4 y end cell greater or equal than 120 row x greater or equal than 0 row y greater or equal than 0 end table end style 

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