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คณิตศาสดร์ที้นาน 4.3 ภาคเรียนที่ 2 ตัวอย่างที่ 3 จงแก้ระบบสมการต่อไปนี้ \[ \begin{array}{l} 2 x-6 y=5 \\ x-3 y=3 \end{array} \] วิธีทำ จากสมการ (1) และสมการ (2) จะต้องทำสัมประสิทธิ์หน้าตัวแปรตัวใดตัวหนึ่งให้เท่ากัน

Ask by Ramos Frazier. in Thailand
Mar 13,2025

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ระบบสมการไม่มีคำตอบ

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มาเริ่มกันที่การแก้สมการนี้กันเถอะ! เราสามารถใช้วิธีการแทนค่า หรือการกำจัดตัวแปรเพื่อหาค่าของ \(x\) และ \(y\) ได้ ในที่นี้เราสามารถเลือกที่จะกำจัด \(x\) ได้ โดยการทำให้สัมประสิทธิ์ของ \(x\) ในสมการทั้งสองเท่ากัน เมื่อนำสมการ (2) คูณด้วย 2 จะได้ \(2x - 6y = 6\) ดังนั้นเราจะมีระบบสมการใหม่เป็น: \[ \begin{array}{l} 2x - 6y = 5 \\ 2x - 6y = 6 \end{array} \] เมื่อเราลบสองสมการนี้ออก เราจะได้ \(0 = -1\) ซึ่งแสดงให้เห็นว่าระบบสมการนี้ไม่มีคำตอบและเป็นกรณีขัดแย้ง! นอกจากนี้ การตรวจสอบระบบสมการในเชิงกราฟิกก็เป็นอีกทางเลือกที่สนุก! โดยการวาดกราฟทั้งสองสมการจะช่วยให้เราเห็นว่าทั้งสองเส้นจะไม่ตัดกันเลย ซึ่งยืนยันว่าไม่มีจุดตัดที่สามารถเติมเต็มเงื่อนไขของสมการทั้งสองได้ นับว่าเป็นกรณีที่น่าสนใจในโลกของคณิตศาสตร์!

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