[CUỘC THI TRÍ TUỆ VICE]
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*Trả lời đúng và hay sẽ được nhận 1-2GP/câu trả lời nha ^^ Hãy giúp chúng mình giải những bài này ^^
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[Toán.C599 _ 29.3.2021]
[Toán.C600 _ 29.3.2021]
\(\left\{{}\begin{matrix}x+2y=2\\mx-y=m\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x+2y=2\\2mx-2y=2m\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2mx+x=2+2m\\x+2y=2\end{matrix}\right.\\ \left\{{}\begin{matrix}x\left(2m+1\right)=2\left(m+1\right)\\x+2y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2\left(m+1\right)}{2m+1}\\\dfrac{2\left(m+1\right)}{2m+1}+2y=2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2\left(m+1\right)}{2m+1}\\2m+2+4my+2y=4m+2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2\left(m+1\right)}{2m+1}\\y\left(4m+2\right)=2m\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2\left(m+1\right)}{2m+1}\\y=\dfrac{2m}{4m+2}\end{matrix}\right.\\ thay.....x,y....vào....ta.....được\\ \dfrac{2\left(m+1\right)}{2m+1}+\dfrac{2m}{4m+2}=1\\ \Leftrightarrow\dfrac{4\left(m+1\right)}{4m+2}+\dfrac{2m}{4m+2}=\dfrac{4m+2}{4m+2}\\ \Rightarrow4m+4+2m=4m+2\\ \Leftrightarrow2m=-2\\ \Leftrightarrow m=-1\\ vậy...m=-1...thì...tm\) \(thay....m=3...vào...ta...có...hpt:\\ \left\{{}\begin{matrix}x+2y=2\\3x-y=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x+2y=2\\6x-2y=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}7x=8\\x+2y=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{8}{7}\\y=\dfrac{3}{7}\end{matrix}\right.\)
\(thay...m=3....ta...có:\\ \left\{{}\begin{matrix}x+2y=2\\3x-y=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x+2y=2\\6x-2y=6\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}7x=8\\x+2y=2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{8}{7}\\y=\dfrac{3}{7}\end{matrix}\right.\\ vậy...với..m=3...thì...hệ....phương....trình....có...nghiệm...duy...nhất\left\{x=\dfrac{8}{7};y=\dfrac{3}{7}\right\}\)
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