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Giải bài 2.13 trang 32 SGK Toán 10 tập 1 – Kết nối tri thức

Biểu diễn miền nghiệm của hệ bất phương trình trên mặt phẳng tọa độ

𓄧Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Kết nối tri thức

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Đề bài

Biểu diễn miền nghiệm của hệ bất phương trình \(\left\{ \begin{array}{l}x + y < 1\\2x - y \ge 3\end{array} \right.\) trên mặt phẳng tọa độ

Phương pháp giải - Xem chi tiết

Biểu diễn các miền nghiệm của từng bất phương trình \(x + y < 1\) và \(2x - y \ge 3\) Bước 1: Vẽ đường thẳng \(ax + by = c\) Bước 2: Lấy điểm một điểm không thuộc đường thẳng \(ax + by = c\) và thay vào bất phương trình cần xác định miền nghiệm. Bước 3: Nếu tọa độ điểm đó thỏa mãn bất phương trình thì miền nghiệm của bất phương trình chứa điểm đó.

Lời giải chi tiết

Xác định miền nghiệm của bất phương trình \(x + y < 1\)+ Vẽ đường thẳng d: x+y=1 (nét đứt) đi qua (0;1) và (1;0)+ Vì 0+0=0 < 1 nên điểm O(0;0) thuộc miền nghiệm của bpt Do đó, miền nghiệm của bất phương trình \(x + y < 1\) là nửa mặt phẳng bờ d chứa gốc tọa độ O.Xác định miền nghiệm của bất phương trình \(2x - y \ge 3\)+ Vẽ đường thẳng d’: \(2x - y = 3\) đi qua (1;-1) và (0;-3)+ Vì 2.0-0=0Do đó, miền nghiệm của bất phương trình \(2x - y \ge 3\) là nửa mặt phẳng bờ d’ không chứa gốc tọa độ O.Vậy miền không bị gạch là miền nghiệm của hệ bất phương trình đã cho (Không  đường thẳng d’).

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