Cho hệ phương trình

D

- Hướng dẫn giải

Đáp án D

Ta có

$$\begin{gathered} \left\{\begin{array}{l}2x-7y=8\\ 1-x+3y=21\end{array}\right.\iff \left\{\begin{array}{l}x=\frac{8+7y}{2}\\ 10.\left(\frac{8+7y}{2}\right)+3y=21\end{array}\right. \\ \iff \left\{\begin{array}{l}x=\frac{8+7y}{2}\\ 40+35y+3y=21\end{array}\right.\iff \left\{\begin{array}{l}x=\frac{{\displaystyle 8+7y}}{{\displaystyle 2}}\\ 38y=-19\end{array}\right. \\ \iff \left\{\begin{array}{l}x=\frac{{\displaystyle 8+7y}}{{\displaystyle 2}}\\ y=-\frac{{\displaystyle 1}}{{\displaystyle 2}}\end{array}\right.\iff \left\{\begin{array}{l}y=-\frac{{\displaystyle 1}}{{\displaystyle 2}}\\ x=\frac{{\displaystyle 9}}{{\displaystyle 4}}\end{array}\right. \end{gathered}$$

Vậy hệ phương trình có nghiệm duy nhất $(x; y)=\left(\frac{9}{4};-\frac{1}{2}\right)\Rightarrow x+y=\frac{7}{4}$