giải các hệ phương trình
9x-6y=4 và 3(4x-3y)=-3x+y+7
3(x+1)+2y=-x và 5(x+y)=-3x+y-5
2(2x+3y)=3(2x-3y)+10 và 4x-3y=4(6y-2x)+3
bài 1: giải các hệ phương trình
1)\(\dfrac{1}{x}\)+\(\dfrac{1}{y}\)=\(\dfrac{1}{2}\)
x+y=9
2) \(\dfrac{2x+1}{4}-\dfrac{y-2}{3}=\dfrac{1}{12}\)
\(\dfrac{x+5}{2}-\dfrac{y+7}{3}=-4\)
3)\(2|x|-y=3\)
\(|x|+y=3\)
4)\(2\left(x+y\right)+\sqrt{x+1}=4\)
\(\left(x+y\right)-3\sqrt{x+1}=-5\)
5) \(\dfrac{7}{2x+y}+\dfrac{4}{2x-y}=74\)
\(\dfrac{3}{2x+y}+\dfrac{2}{2x-y}=32\)
6)\(\dfrac{1}{x}+\dfrac{3}{2y+1}=2\)
\(\dfrac{2}{x}+\dfrac{4}{2y+1}=2\)
7) \(\dfrac{1}{x}+\dfrac{1}{y}=2\)
\(\dfrac{3}{x}-\dfrac{1}{y}=2\)
8)\(\dfrac{1}{x+2}+\dfrac{3}{2y-1}=4\)
\(\dfrac{4}{x+2}-\dfrac{1}{2y-1}=3\)
9)\(\dfrac{4}{x+y} +\dfrac{1}{y-1}=5\)
\(\dfrac{1}{x+y}-\dfrac{2}{y-1}=-1\)
10)\(\dfrac{7}{\sqrt{2x+3}}-\dfrac{4}{\sqrt{3}-y}=\dfrac{5}{3}\)
\(\dfrac{5}{\sqrt{2x+3}}+\dfrac{3}{\sqrt{3-y}}=\dfrac{13}{6}\)
11)\(\dfrac{3x}{x-1}-\dfrac{2}{y+2}=4\)
\(\dfrac{2x}{x-1}+\dfrac{1}{y+2}=5\)
12) \(\dfrac{7}{\sqrt{x}-7}-\dfrac{4}{\sqrt{y}+6}=\dfrac{5}{3}\)
\(\dfrac{5}{\sqrt{x}-7}+\dfrac{3}{\sqrt{y}+6}2\dfrac{1}{6}\)
13) \(3\sqrt{x-1}+2\sqrt{y}=13\)
\(2\sqrt{x-1}-\sqrt{y}=4\)
14) 6x + 6y = 5xy
\(\dfrac{4}{x}-\dfrac{3}{y}=1\)
Giải hệ phương trình
\(\left\{{}\begin{matrix}4\left(2x-y+3\right)-3\left(x-2y+3\right)=48\\3\left(3x-4y+3\right)+4\left(4x-2y-9\right)=48\end{matrix}\right.\)
\(\left\{{}\begin{matrix}6\left(x+y\right)=8+2x-3y\\5\left(y-x\right)=5+3x+2y\end{matrix}\right.\)
\(\left\{{}\begin{matrix}-2\left(2x+1\right)+1,5=3\left(y-2\right)-6x\\11,5-4\left(3-x\right)=2y-\left(5-x\right)\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{8x-5y-3}{7}+\dfrac{11y-4x-7}{5}=12\\\dfrac{9x+4y-13}{5}-\dfrac{3\left(x-2\right)}{4}=15\end{matrix}\right.\)
\(\left\{{}\begin{matrix}2\sqrt{3}x-\sqrt{5}y=2\sqrt{6}-\sqrt{15}\\3x-y=3\sqrt{2}-\sqrt{3}\end{matrix}\right.\)
Giải hệ phương trình sau bằng phương pháp thế
a)
\(\left\{{}\begin{matrix}\sqrt{5}+2)x+y=3-\sqrt{5}\\-x+2y=6-2\sqrt{5}\end{matrix}\right.\)
b)
\(\left\{{}\begin{matrix}5\left(x+2y\right)=3x-1\\2x+4=3\left(x-5y\right)-12\end{matrix}\right.\)
Giải hệ phương trình sau bằng phương pháp thế
1) \(\left\{{}\begin{matrix}x-2y=4\\-2x+5y=-3\end{matrix}\right.\)
2) \(\left\{{}\begin{matrix}2x+y=10\\5x-3y=3\end{matrix}\right.\)
3) \(\left\{{}\begin{matrix}x+2y=4\\-3x+y=7\end{matrix}\right.\)
Giải các hệ phương trình sau bằng cách đặt ẩn số phụ:
a) \(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{4}{5}\\\dfrac{1}{x}-\dfrac{1}{y}=\dfrac{1}{5}\end{matrix}\right.\);
b) \(\left\{{}\begin{matrix}\dfrac{15}{x}-\dfrac{7}{y}=9\\\dfrac{4}{x}+\dfrac{9}{y}=35\end{matrix}\right.\);
c) \(\left\{{}\begin{matrix}\dfrac{1}{x+y}+\dfrac{1}{x-y}=\dfrac{5}{8}\\\dfrac{1}{x+y}-\dfrac{1}{x-y}=-\dfrac{3}{8}\end{matrix}\right.\);
d) \(\left\{{}\begin{matrix}\dfrac{4}{2x-2y}+\dfrac{5}{3x+y}=-2\\\dfrac{3}{3x+y}-\dfrac{5}{2x-3y}=21\end{matrix}\right.\);
e) \(\left\{{}\begin{matrix}\dfrac{7}{x-y+2}-\dfrac{5}{x+y-1}=4,5\\\dfrac{3}{x-y+2}+\dfrac{2}{x+y-1}=4\end{matrix}\right.\).
1.Giải hệ phương trình:
a.\(\left\{{}\begin{matrix}2\sqrt{2}x+y=2\sqrt{2}\\7x-3y=7\end{matrix}\right.\)
b.\(\left\{{}\begin{matrix}7x+y=-\frac{1}{7}\\-\frac{4}{3}x-2y=1\frac{1}{3}\end{matrix}\right.\)
c.\(\left\{{}\begin{matrix}2\sqrt{5}x+3y=\sqrt{2}\\\sqrt{5}x-y=3\sqrt{2}\end{matrix}\right.\)
d.\(\left\{{}\begin{matrix}\frac{2}{x}+\frac{3}{y}=-5\\\frac{3}{x}-\frac{4}{y}=1\end{matrix}\right.\)
e.\(\left\{{}\begin{matrix}-\frac{5}{3x+1}+\frac{7}{2x+1}=\frac{5}{7}\\\frac{1}{3x+1}-\frac{1}{2y-3}=\frac{2}{7}\\\end{matrix}\right.\)
g.\(\left\{{}\begin{matrix}2x^2+5y^2=129\\-3x^2+y^2=13\end{matrix}\right.\)
a) \(\left\{{}\begin{matrix}2x+4=0\\4x+2y=-3\end{matrix}\right.\) c)\(\left\{{}\begin{matrix}\left(x-15\right).\left(y+2\right)=x.y\\\left(x+15\right).\left(y-1\right)=x.y\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}2x+4=y\\x+2y=-3\end{matrix}\right.\) d) \(\left\{{}\begin{matrix}\frac{1}{x}+\frac{1}{y}=5\\\frac{2}{x}+\frac{5}{y}=7\end{matrix}\right.\) tính bằng phương pháp cộng dại số
Giaỉ hệ phương trình sau bằng phương pháp thế
a)\(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{2};\dfrac{3}{x}-\dfrac{4}{y}=-1\)
b)\(\dfrac{3}{2x-y}-\dfrac{6}{x+y}=-1;\dfrac{1}{2x-y}-\dfrac{1}{x+y}=0\)
c)\(\dfrac{5x}{x+1}+\dfrac{y}{y-3}=27;\dfrac{2x}{x+1}-\dfrac{3y}{y-3}=4\)
d)\(\dfrac{7}{x+2}+\dfrac{3}{y}=2;\dfrac{4}{x+2}-\dfrac{1}{y}=\dfrac{5}{2}\)
e)\(\dfrac{2x}{x+4}+\dfrac{2y}{2y-3}=27;\dfrac{2x}{x+4}-\dfrac{6y}{2y-3}=4\)
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