Bài 1
a)\(\left\{{}\begin{matrix}2x+y=3\\x-y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(2x+y\right)+x-y=9\\x-y=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x=9\\x-y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-9\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}\frac{1}{x}+\frac{1}{y}=\frac{1}{16}\\\frac{3}{x}+\frac{6}{y}=\frac{1}{4}\end{matrix}\right.\) đặt \(\frac{1}{x}=a,\frac{1}{y}=b\)
\(\Rightarrow\left\{{}\begin{matrix}a+b=\frac{1}{16}\\3a+6b=\frac{1}{4}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3a+3b=\frac{3}{16}\\3a+6b=\frac{1}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=\frac{1}{24}\\b=\frac{1}{48}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\frac{1}{x}=\frac{1}{24}\\\frac{1}{y}=\frac{1}{48}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=24\\y=48\end{matrix}\right.\)
Bài 2
Gọi số giá sách ban đầu ở mỗi giá sách là a, b ( a,b < 450)
Hai giá sách có 450 quyển
\(x+y=450\left(1\right)\)
Chuyển 50 quyển sách từ giá T1 sang giá T2 thì giá T2=4/5 giá T1
\(\Rightarrow y+50=\frac{4}{5}\left(x-50\right)\)
\(\Rightarrow y+50=\frac{4}{5}x-40\)
\(\Rightarrow\frac{4}{5}x-y=90\left(2\right)\)
Từ 1 và 2 ta có hpt
\(\left\{{}\begin{matrix}x+y=450\\\frac{4}{5}x-y=90\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=300\\y=150\end{matrix}\right.\)(t/m)
Vậy..........
Bài 3
\(\left\{{}\begin{matrix}2x+y=5m-1\\x-2y=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2\left(2+2y\right)+y=5m-1\\x=2+2y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4y+4+y=5m-1\\x=2y+2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}5y=5m-5\\x=2y+2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}y=\frac{5m-5}{5}\\x=2y+2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y=m-1\\x=2m\end{matrix}\right.\)
\(x+y=5\Rightarrow2m+m-1=5\)
\(\Rightarrow3m=6\Rightarrow m=2\)
