Nghiệm của hệ \(\left\{\begin{array}{l} 4 x-3 y+5(x-y)=1 \\ 2 x-4(2 y-1)=1 \end{array}\right.\) là đáp án:

* Hướng dẫn giải

Ta có:

\(\left\{\begin{array}{l} 4 x-3 y+5(x-y)=1 \\ 2 x-4(2 y-1)=1 \end{array}\right.\)

\(\begin{array}{l} \Leftrightarrow\left\{\begin{array}{l} 4 x-3 y+5(x-y)=1 \\ 2 x-4(2 y-1)=1 \end{array} \Leftrightarrow\left\{\begin{array}{l} 4 x-3 y+5 x-5 y=1 \\ 2 x-8 y+4=1 \end{array}\right.\right. \\ \Leftrightarrow\left\{\begin{array}{l} 9 x-8 y=1 \\ 2 x-8 y=-3 \end{array} \Leftrightarrow\left\{\begin{array}{l} 9 x-8 y=1 \\ x=4 y-\frac{3}{2} \end{array} \Leftrightarrow\left\{\begin{array}{l} 9\left(4 y-\frac{3}{2}\right)-8 y=1 \\ x=4 y-\frac{3}{2} \end{array}\right.\right.\right. \end{array}\)

\(\Leftrightarrow\left\{\begin{array}{l} 36 y-\frac{27}{2}-8 y=1 \\ x=4 y-\frac{3}{2} \end{array} \Leftrightarrow\left\{\begin{array}{l} 28 y=1+\frac{27}{2} \\ x=4 y-\frac{3}{2} \end{array} \Leftrightarrow\left\{\begin{array}{l} y=\frac{29}{56} \\ x=4 \cdot\left(\frac{29}{56}\right)-\frac{3}{2} \end{array}\right.\right.\right.\)

\(\Leftrightarrow\left\{\begin{array}{l} y=\frac{29}{56} \\ x=\frac{4}{7} \end{array}\right.\)

Vậy, nghiệm của hệ phương trình là: \(\left(\frac{4}{7} ; \frac{29}{56}\right)\)