Đáp án Toán 10 cánh diều C2 bài 1. Bất phương trình bậc nhất hai ẩn

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BÀI TẬP CUỐI CHƯƠNG I

I. BẤT PHƯƠNG TRÌNH BẬC NHẤT HAI ẨN

Bài 1: Tìm bất phương trình bậc nhất hai ẩn trong...

Đáp án:

1. a) 5x + 3y < 20 là bất phương trình bậc nhất hai ẩn.

Chọn x = 1; y = 1, ta có:

5.1 + 3.1 = 8 < 20 là mệnh đề đúng.

Vậy (1; 1) là nghiệm của bất phương trình.

1. b) 3x - > 2 không phải là bất phương trình bậc nhất hai ẩn vì có ẩn y ở mẫu.

II. BIỂU DIỄN MIỀN NGHIỆM CỦA BẤT PHƯƠNG TRÌNH BẬC NHẤT HAI ẨN

Bài 1: Biểu diễn miền nghiệm của mỗi bất phương trình sau...

Đáp án:

1. a) x - 2y < 4

+ Vẽ đường thẳng d: x – 2y = 4

Cho x = 0 thì y = – 2, cho y = 0 thì x = 4. Đường thẳng d đi qua 2 điểm (0; – 2) và (4; 0). 

+ Lấy điểm O (0; 0). Ta có: 0 – 0 = 0 < 4.

Vậy miền nghiệm của bất phương trình x – 2y < 4 là nửa mặt phẳng không bị gạch chứa điểm O (0; 0) không kể đường thẳng d. 

1. b) x + 3y ≥ 6

+ Vẽ đường thẳng d: x + 3y = 6

Cho x = 0 thì y = 2, cho y = 0 thì x = 6, do đó đường thẳng d đi qua hai điểm (0; 2) và (6; 0). 

+ Lấy điểm O (0; 0). Ta có: 0 + 3.0 = 0 < 6. 

Vậy miền nghiệm của bất phương trình x + 3y ≥ 6 là nửa mặt phẳng không bị gạch không chứa điểm O (0; 0) kể cả đường thẳng d. 

BÀI TẬP CUỐI SGK

Bài tập 1: Cặp số nào sau đây là nghiệm của bất phương trình...

Đáp án:

Ta có: 2x – 3y < 3 (1).

2. a) Thay x = 0, y = – 1 vào bất phương trình (1) ta được: 2. 0 – 3. (– 1) < 3 

⇔ 3 < 3 là mệnh đề sai.

Vậy cặp số (0; – 1) không phải là nghiệm của bất phương trình đã cho. 

2. b) Tương tự ta có: 2. 2 – 3. 1 = 4 – 3 = 1 < 3 là mệnh đề đúng.

Vậy cặp số (2; 1) là một nghiệm của bất phương trình đã cho. 

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