1. \(\left\{{}\begin{matrix}4x-2y=3.\\6x-3y=5.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}12x-6y=9.\\12x-6y=10.\end{matrix}\right.\)\(\Leftrightarrow x\in\phi.\)
2. \(\left\{{}\begin{matrix}2x+3y=5.\\4x+6y=10.\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}8x+12y=20.\\8x+12y=20.\end{matrix}\right.\)\(\Leftrightarrow x\in\phi.\)
3. \(\left\{{}\begin{matrix}3x-4y+2=0.\\5x+2y=14.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}3x-4y=-2.\\5x+2y=14.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}3x-4y=-2.\\10x+4y=28.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}3x-4y=-2.\\13x=26.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}y=2.\\x=2.\end{matrix}\right.\)
4. \(\left\{{}\begin{matrix}2x+5y=3.\\3x-2y=14.\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x+15y=9.\\6x-4y=28.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}2x+5y=3.\\19y=-19.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=4.\\y=-1.\end{matrix}\right.\)
7. \(\left\{{}\begin{matrix}\dfrac{x}{y}=\dfrac{2}{3}.\\x+y-10=0.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}3x-2y=0.\\x+y=10.\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-2y=0.\\3x+3y=30.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x+y=10.\\-5y=-30.\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4.\\y=6.\end{matrix}\right.\)