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Giải bài 3 trang 16 vở thực hành Toán 9

Giải các hệ phương trình sau bằng phương pháp thế: a) (left{ begin{array}{l}2x - y = 1\x - 2y = - 1end{array} right.); b) (left{ begin{array}{l}0,5x - 0,5y = 0,5\1,2x - 1,2y = 1,2end{array} right.); c) (left{ begin{array}{l}x + 3y = - 2\5x - 4y = 28end{array} right.).

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Giải các hệ phương trình sau bằng phương pháp thế: a) \(\left\{ \begin{array}{l}2x - y = 1\\x - 2y =  - 1\end{array} \right.\); b) \(\left\{ \begin{array}{l}0,5x - 0,5y = 0,5\\1,2x - 1,2y = 1,2\end{array} \right.\); c) \(\left\{ \begin{array}{l}x + 3y =  - 2\\5x - 4y = 28\end{array} \right.\).

Phương pháp giải - Xem chi tiết

Giải phương trình bằng phương pháp thế: Bước 1: Từ một phương trình của hệ, biểu diễn một ẩn theo ẩn kia rồi thế vào phương trình còn lại của hệ để được phương trình chỉ còn chứa một ẩn. Bước 2: Giải phương trình một ẩn vừa nhận được, từ đó suy ra nghiệm của hệ đã cho.

Lời giải chi tiết

a) Từ phương trình thứ nhất của hệ ta có \(y = 2x - 1\). Thế vào phương trình thứ hai của hệ, ta được \(x - 2\left( {2x - 1} \right) =  - 1\) hay \( - 3x + 2 =  - 1\), suy ra \(x = 1\). Từ đó, \(y = 2.1 - 1 = 1\). Vậy hệ phương trình đã cho có nghiệm là (1; 1). b) Từ phương trình thứ nhất của hệ ta có \(y = x - 1\). Thế vào phương trình thứ hai của hệ, ta được \(1,2x - 1,2\left( {x - 1} \right) = 1,2\) hay \(0x = 0\). Ta thấy mọi giá trị của x đều thỏa mãn hệ thức trên. Với giá trị tùy ý của x, giá trị của y được tính nhờ hệ thức \(y = x - 1\). Vậy hệ phương trình đã cho có nghiệm là \(\left( {x;x - 1} \right)\) với \(x \in \mathbb{R}\) tùy ý. c) Từ phương trình thứ nhất của hệ ta có \(x =  - 3y - 2\). Thế vào phương trình thứ hai của hệ, ta được \(5\left( { - 3y - 2} \right) - 4y = 28\) hay \( - 19y - 10 = 28\), suy ra \(y =  - 2\). Từ đó \(x =  - 3.\left( { - 2} \right) - 2 = 4\) Vậy hệ phương trình đã cho có nghiệm là (4; -2).

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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