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Giải bài 3 trang 14 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Xác định a, b để đồ thị hàm số y = ax + b đi qua hai điểm A và B trong mỗi trường hợp sau: a) A(1;1) và B(3;7); b) A(2;1) và B(4; -3).

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

Toán - Văn - Anh
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Đề bài

Xác định a, b để đồ thị hàm số y = ax + b đi qua hai điểm A và B trong mỗi trường hợp sau: a) A(1;1) và B(3;7); b) A(2;1) và B(4; -3).

Phương pháp giải - Xem chi tiết

ജThay toạ độ từng điểm vào y = ax + b để lập hệ phương trình

Giải hệ phương trình bằng phương pháp thế

ꦬB1: Từ 1 phương trình của hệ, ta biểu diễn ẩn này theo ẩn kia, rồi thế vào phương trình còn lại của hệ để nhận được một phương trình một ẩn.

🎉B2: Giải phương trình một ẩn đó rồi suy ra nghiệm của hệ.

Giải hệ phương trình bằng phương pháp cộng đại số

ꦚB1: Nhân hai vế của mỗi phương trình với một số thích hợp (nếu cần) sao cho các hệ số của một ẩn nào đó trong hai phương trình của hệ bằng nhau hoặc đối nhau.

🔜B2: Cộng hay trừ từng vế hai phương trình của hệ để được một phương trình một ẩn và giải phương trình đó.

❀B3: Thế giá trị của ẩn vừa tìm được ở B2 và một trong hai phương trình của hệ đã cho để tìm giá trị của ẩn còn lại. Kết luận nghiệm của hệ.

Lời giải chi tiết

a) Thay toạ độ điểm A(1;1) và B(3;7) vào y = ax + b, ta được hệ phương trình \(\begin{array}{l}\left\{ {\begin{array}{*{20}{c}}{a + b = 1}\\{3a + b = 7}\end{array}} \right.\\\left\{ {\begin{array}{*{20}{c}}{a + b = 1}\\{ - 2a =  - 6}\end{array}} \right.\\\left\{ {\begin{array}{*{20}{c}}{b =  - 2}\\{a = 3}\end{array}} \right.\end{array}\) b) Thay toạ độ điểm A(2;1) và B(4; -3) vào y = ax + b, ta được hệ phương trình \(\begin{array}{l}\left\{ {\begin{array}{*{20}{c}}{2a + b = 1}\\{4a + b =  - 3}\end{array}} \right.\\\left\{ {\begin{array}{*{20}{c}}{2a + b = 1}\\{ - 2a = 4}\end{array}} \right.\\\left\{ {\begin{array}{*{20}{c}}{b = 5}\\{a =  - 2}\end{array}} \right.\end{array}\)

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

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