解方程

\(\bar{x}\)	\(\bar{y}\)	\(\bar{w}\)	\(\sum\limits_{i=1}^{8}\)\((x_i-\bar{x})^2\)	\(\sum\limits_{i=1}^{8}{(w_i-\bar{w})^2}\)	\(\sum\limits_{i=1}^{8}{(x_i-\bar{x})\cdot(y_i-\bar{y})}\)	\(\sum\limits_{i=1}^{8}{(w_i-\bar{w})\cdot(y_i-\bar{y})}\)
\(46.6\)	\(563\)	\(6.8\)	\(289.8\)	\(1.6\)	\(1469\)	\(108.8\)

\(x\)	\((-\infty,0)\)	\(0\)	\((0,1)\)	\((1,\cfrac{3}{2})\)	\(\cfrac{3}{2}\)	\((\cfrac{3}{2},+\infty)\)
\(f'(x)\)	+	0	-	-	0	+
\(f(x)\)	\(\nearrow\)	\(1\)	\(\searrow\)	\(\searrow\)	\(17.9\)	\(\nearrow\)

典例剖析

[初二习题]甲、乙两个人解关于\(x\)、\(y\)的方程组\(\left\{\begin{array}{l}{mx+by=2}\\{cx-7y=8}\end{array}\right.,\) 已知甲正确的解得\(\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.,\) 而乙由于把 \(c\) 看错了，解得\(\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.,\) 那么\(m\)、\(b\)、\(c\)的值分别是多少？乙把\(c\)看成了多少？

分析：由于甲是正确地解得方程的解，\(\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.,\) 故其满足方程组，

即\(\left\{\begin{array}{l}{3m-2b=2}\\{3c-7\times(-2)=8}\end{array}\right.,\) 解得\(c=-2\)；

由上可以得到，\(3m-2b=2\)①；

又由于乙将系数看错，解得方程的解，\(\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.,\) 故其也满足方程组，

即\(\left\{\begin{array}{l}{-2m+2b=2}\\{-2c-7\times(-2)=8}\end{array}\right.,\) 解得\(c=-11\)；

由上可以得到，\(-2m+2b=2\)②；

联立①②，得到\(m=4\)， \(b=5\)，

故\(m=4\)， \(b=5\)，\(c=-2\)， 乙把\(c\)看成了\(c=11\).