![](https://imgix2.ruangguru.com/assets/miscellaneous/png_anx5qa_4400.PNG)
Untuk menentukan sistem pertidaksamaan yang memenuhi daerah penyelesaian di atas, kita perlu menentukan persamaan semua garis yang membatasi daerah penyelesaian tersebut.
Perhatikan garis lurus yang melalui titik
dan
. Persamaan garis tersebut adalah
![begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator y minus 0 over denominator 5 minus 0 end fraction end cell equals cell fraction numerator x minus 10 over denominator 0 minus 10 end fraction end cell row cell y over up diagonal strike 5 to the power of 1 end cell equals cell fraction numerator x minus 10 over denominator up diagonal strike negative 10 end strike to the power of negative 2 end exponent end fraction end cell row cell negative 2 y end cell equals cell x minus 10 end cell row cell negative x minus 2 y end cell equals cell negative 10 end cell row cell x plus 2 y end cell equals cell 10 number space number space number space number space number space horizontal ellipsis left parenthesis 1 right parenthesis end cell end table end style](data:image/png;base64,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)
Selanjutnya, untuk menentukan tanda pertidaksamaan yang sesuai, kita akan melakukan uji titik. Perhatikan bahwa garis lurus tersebut penuh (tidak putus-putus) dan daerah penyelesaian memuat titik
. Jika disubstitusikan ke persamaan
, diperoleh
.
Akibatnya, pertidaksamaan yang memenuhi adalah
.
Berikutnya, karena daerah penyelesaian berada di antara garis
dan
(kedua garis juga tidak putus-putus), maka pertidaksamaan yang memenuhi adalah
.
Terakhir, karena daerah penyelesaian berada di atas garis
(garis tersebut juga tidak putus-putus), maka pertidaksamaan yang memenuhi adalah
.
Dengan demikian, sistem pertidaksamaan yang memenuhi daerah penyelesaian pada gambar di atas adalah
![begin mathsize 14px style open curly brackets table attributes columnalign left end attributes row cell x plus 2 y less or equal than 10 end cell row cell 2 less or equal than x less or equal than 5 end cell row cell y greater or equal than negative 3 end cell end table close end style](data:image/png;base64,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)