সরল সহসমীকরণ (৬.১)

অষ্টম শ্রেণি (মাধ্যমিক ২০২৫) - গণিত সরল সহসমীকরণ | - | NCTB BOOK
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x + y = 5 একটি সমীকরণ। এখানে, x ও y দুইটি অজানা রাশি বা চলক। এই চলক দুইটি একঘাতবিশিষ্ট। এরূপ সমীকরণ সরল সমীকরণ।

এখানে, যে সংখ্যাদ্বয়ের যোগফল 5 সেই সংখ্যা দ্বারাই সমীকরণটি সিদ্ধ হবে। যেমন, x = 4, y = 1; বা, x = 3, y = 2; বা, x = 2, y = 3; বা, x = 1, y = 4, ইত্যাদি, এরূপ অসংখ্য সংখ্যাযুগল দ্বারা সমীকরণটি সিদ্ধ হবে।

আবার, x – y = 3 এই সমীকরণটি বিবেচনা করলে দেখতে পাই, সমীকরণটি x = 4, y=1 বা x = 5, y = 2 _বা_ x = 6, y = 3 বা x = 7, y = 4 বা x = 8, y = 5 বা x = 2, y = -1 বা x = 1, y = -2, x = 0, y = - 3 ... ইত্যাদি অসংখ্য সংখ্যাযুগল দ্বারা সিদ্ধ হয়।

এখানে, x + y = 5 এবং x - y = 3 সমীকরণ দুইটি একত্রে বিবেচনা করলে উভয় সমীকরণ হতে প্রাপ্ত সংখ্যাযুগলের মধ্যে x = 4, y = 1 দ্বারা উভয় সমীকরণ যুগপৎ সিদ্ধ হয়।

চলকের মান দ্বারা একাধিক সমীকরণ সিদ্ধ হলে, সমীকরণসমূহকে একত্রে সহসমীকরণ বলা হয় এবং চলক একঘাত বিশিষ্ট হলে সহসমীকরণকে সরল সহসমীকরণ বলে।

চলকদ্বয়ের যে মান দ্বারা সহসমীকরণ যুগপৎ সিদ্ধ হয়, এদেরকে সহসমীকরণের মূল বা সমাধান বলা হয় । এখানে x + y = 5 এবং x - y = 3 সমীকরণ দুইটি সহসমীকরণ। এদের একমাত্র সমাধান x=4, y=1_ যা (x, y) = ( 4, 1 ) দ্বারা প্রকাশ করা যায়।

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Request history8.2.28PHP Version95.56msRequest Duration9MBMemory UsageGET academy/{slug}Route
    • Booting (29.35ms)time
    • Application (66.2ms)time
    • 1 x Application (69.28%)
      66.20ms
      1 x Booting (30.72%)
      29.35ms
      49 templates were rendered
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      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • academy.include.sidebarSubListsidebarSubList.blade.php#?blade
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      • laravelpwa::metameta.blade.php#?blade
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      • layouts.footerfooter.blade.php#?blade
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      • common.includes.promotion_modalpromotion_modal.blade.php#?blade
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      • common.script.promotion_functionspromotion_functions.blade.php#?blade
      uri
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      App\Http\Controllers\Academy\SubjectController@chapter
      namespace
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      as
      academy.subject.chapter
      file
      app/Http/Controllers/Academy/SubjectController.php:102-110
      20 statements were executed (2 duplicates)Show only duplicates35.62ms
      • SubjectRepository.php#94satt_satt_mobile_app160μsselect `id`, `main_category_id`, `parent_id`, `show_content` from `subjects` where `slug` = 'সরল-সহসমীকরণ' and `subjects`.`deleted_at` is null limit 1
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        • app/Repositories/SubjectRepository.php:94
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        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:91
        • app/Services/SubjectService.php:32
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        • app/Services/SubjectService.php:43
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
        • vendor/laravel/framework/src/Illuminate/Routing/Route.php:266
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:38
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:60
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        • app/Repositories/SubjectRepository.php:285
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        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
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        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:285
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        Backtrace
        • app/Repositories/SubjectRepository.php:122
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Repositories/SubjectRepository.php:121
        • app/Services/SubjectService.php:60
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        Backtrace
        • app/Repositories/SubjectRepository.php:125
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        • app/Repositories/SubjectRepository.php:121
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        • app/Repositories/SubjectRepository.php:137
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
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        • app/Repositories/SubjectRepository.php:136
        • app/Services/SubjectService.php:61
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        Backtrace
        • app/Repositories/SubjectRepository.php:140
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:136
        • app/Services/SubjectService.php:61
      • SubjectRepository.php#140satt_satt_mobile_app110μsselect `id`, `description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (7877) and `subject_descriptions`.`deleted_at` is null
        Backtrace
        • app/Repositories/SubjectRepository.php:140
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:136
        • app/Services/SubjectService.php:61
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:38
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:60
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        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
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        Backtrace
        • app/Repositories/SubjectRepository.php:325
        • app/Services/SubjectService.php:76
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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        Backtrace
        • app/Repositories/SubjectRepository.php:340
        • app/Services/SubjectService.php:77
        • app/Http/Controllers/Academy/SubjectController.php:105
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        Backtrace
        • app/Services/SubjectService.php:82
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