Bài 20 (SGK trang 19)

Gửi bởi: Sách Giáo Khoa Vào 26 tháng 12 2018 lúc 11:13:45

Câu hỏi

Giải các hệ phương trình sau bằng phương pháp cộng đại số:

a) $\left\{{}\begin{matrix}3x+y=3\\2x-y=7\end{matrix}\right.;$ b) $\left\{{}\begin{matrix}2x+5y=8\\2x-3y=0\end{matrix}\right.;$ c) $\left\{{}\begin{matrix}4x+3y=6\\2x+y=4\end{matrix}\right.;$

d) $\left\{{}\begin{matrix}2x+3y=-2\\3x-2y=-3\end{matrix}\right.;$ e) $\left\{{}\begin{matrix}0,3x+0,5y=3\\1,5x-2y=1,5\end{matrix}\right..$

Hướng dẫn giải

a) $\left\{\begin{matrix} 3x + y =3 & & \\ 2x - y = 7 & & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} 5x =10 & & \\ 2x -y = 7& & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} x =2 & & \\ y = 2x-7& & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} x =2 & & \\ y = -3& & \end{matrix}\right.$

b) $\left\{\begin{matrix} 2x + 5y =8 & & \\ 2x - 3y = 0& & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} 2x + 5y =8 & & \\ 8y = 8& & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} 2x + 5y =8 & & \\ y = 1& & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} x =\frac{3}{2} & & \\ y = 1& & \end{matrix}\right.$

c) $\left\{\begin{matrix} 4x + 3y =6 & & \\ 2x + y = 4& & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} 4x + 3y =6 & & \\ 4x + 2y =8& & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} 4x + 3y =6 & & \\ y = -2& & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} x =3 & & \\ y = -2& & \end{matrix}\right.$

d) $\left\{\begin{matrix} 2x + 3y =-2 & & \\ 3x -2y = -3& & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} 6x - 9y = -6 & & \\ 6x - 4y = -6& & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} 6x - 9y = -6 & & \\ -5y = 0& & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} x = -1 & & \\ y = 0 & & \end{matrix}\right.$

e) $\left\{\begin{matrix} 0,3x + 0,5y =3 & & \\ 1,5x -2y = 1,5& & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} 1,5x + 2,5y=15 & & \\ 1,5x - 2y = 1,5 & & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} 1,5x + 2,5y=15 & & \\ 4,5y = 13,5 & & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} 1,5x =15 -2, 5 . 3& & \\ y = 3 & & \end{matrix}\right.$ $\Leftrightarrow$ $\left\{\begin{matrix} 1,5x =7,5& & \\ y = 3 & & \end{matrix}\right.$