第12讲 方程与方程组综合

⑴解方程组：$\{\begin{array}{c}x(y+z+x)=18\\ y(x+z+y)=12\\ z(x+y+z)=6\end{array}$

⑵解方程组：$\{\begin{array}{c}xy=2\\ yz=6\\ zx=12\end{array}$

⑶解方程组：$\{\begin{array}{c}xy+xz=27\\ yz+xy=32\\ xz+yz=35\end{array}$．

解方程组：$\{\begin{array}{c}\frac{xy}{x+y}=\frac{6}{5}\\ \frac{xz}{x+z}=\frac{12}{7}\\ \frac{yz}{y+z}=\frac{4}{3}\end{array}$．

解方程组：$\{\begin{array}{c}\frac{x(y+1)}{x+y+1}=\frac{6}{5}\\ \frac{x(z+2)}{x+z+2}=\frac{12}{7}\\ \frac{(y+1)(z+2)}{y+z+3}=\frac{4}{3}\end{array}$．

⑴解方程组：$\{\begin{array}{c}x+y=xy\\ y+z=2yz\\ z+x=5zx\end{array}$

⑵解方程组：$\{\begin{array}{c}xy+x+y=1\\ yz+y+z=5\\ zx+z+x=2\end{array}$．

⑴解方程组：$\{\begin{array}{c}{\left(x+y\right)}^2-2xy-x^2{y}^2=2\\ x+y-xy=4\end{array}$．

⑵解方程组：$\{\begin{array}{c}x+y+\frac{9}{x}+\frac{4}{y}=10\\ \left(x^2+9\right)\left(y^2+4\right)=24xy\end{array}$

解方程组：$\{\begin{array}{c}\sqrt[3]{x+1}+\sqrt[3]{y-1}=2\\ x+y=26\end{array}$．

方程组$\{\begin{array}{c}x+y+z=9\\ x^2+y^2+z^2=41\\ x^3+y^3+z^3=189\end{array}$的解共有组．

⑴已知关于$x,y$的方程组$\{\begin{array}{c}{y}^2=2x\\ y=kx+1\end{array}$有两组不相等的 ，求$k$的取值范围．

⑵关于$x,y$的方程组$\{\begin{array}{c}{y}^2-x=3\\ y=-mx+2\end{array}$只有一组实数解，则实数$m$的值是$\_\_\_\_\_\_\_$．

⑶关于$x,y$的方程组$\{\begin{array}{c}x-\sqrt{y-2}=0\\ kx-y-2k-10=0\end{array}$只有一组解，求$k$的取值范围 ．

解方程组：$\{\begin{array}{c}\frac{1}{x}+\frac{1}{y+z}=\frac{1}{2}\\ \frac{1}{y}+\frac{1}{z+x}=\frac{1}{3}\\ \frac{1}{z}+\frac{1}{x+y}=\frac{1}{4}\end{array}$．

解方程组：$\{\begin{array}{c}\sqrt{4x+5}+\sqrt{4y+12}=7\\ \sqrt{4y+5}+\sqrt{4x+12}=7\end{array}$．

1. 解方程组：$\{\begin{array}{c}xy=3\\ yz=2\\ zx=6\end{array}$

2. 解方程组： $\{\begin{array}{c}xy+xz=8-x^2\\ yx+yz=12-y^2\\ zy+zx=-4-x^2\end{array}$

3. 解方程组：$\{\begin{array}{c}\frac{y}{x}=2y-1\\ \frac{z}{y}=3z-1\\ \frac{x}{z}=4x-1\end{array}$

4. 解方程组： $\{\begin{array}{c}xy+x+y+3=0\\ yz+y+z+7=0\\ zx+z+x-11=0\end{array}$

5. 解方程组$\{\begin{array}{c}x+y=13\\ \sqrt{x}+\sqrt{y}=5\end{array}$

1. 解方程组：$\{\begin{array}{c}xy=2(x+y)\\ yz=3(y+z)\\ zx=4(x+z)\end{array}$．

2. 已知$a-b=4$，$ab+c^2+4=0$，则$a+b=$ ．