题目内容
2.若关于x、y的二元一次方程组$\left\{\begin{array}{l}{3x+my=16}\\{2x+ny=15}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=7}\\{y=3}\end{array}\right.$,则关于x、y的二元一次方程组$\left\{\begin{array}{l}{3(x+y)-m(x-y)=16}\\{2(x+y)+n(x-y)=15}\end{array}\right.$ 的解是$\left\{\begin{array}{l}{x=5}\\{y=2}\end{array}\right.$.分析 本题先代入解求出得$\left\{\begin{array}{l}{m=-\frac{5}{3}}\\{n=\frac{1}{3}}\end{array}\right.$,再将其代入二元一次方程组$\left\{\begin{array}{l}{3(x+y)-m(x-y)=16}\\{2(x+y)+n(x-y)=15}\end{array}\right.$,解出即可.
解答 解:把$\left\{\begin{array}{l}{x=7}\\{y=3}\end{array}\right.$代入二元一次方程组$\left\{\begin{array}{l}{3x+my=16}\\{2x+ny=15}\end{array}\right.$,
解得:$\left\{\begin{array}{l}{m=-\frac{5}{3}}\\{n=\frac{1}{3}}\end{array}\right.$,
把$\left\{\begin{array}{l}{m=-\frac{5}{3}}\\{n=\frac{1}{3}}\end{array}\right.$代入二元一次方程组$\left\{\begin{array}{l}{3(x+y)-m(x-y)=16}\\{2(x+y)+n(x-y)=15}\end{array}\right.$,
解得:$\left\{\begin{array}{l}{x=5}\\{y=2}\end{array}\right.$,
故答案为:$\left\{\begin{array}{l}{x=5}\\{y=2}\end{array}\right.$.
点评 本题主要考查二元一次方程组的解法,关键是熟练掌握二元一次方程组的解法即代入消元法和加减消元法.
| 类别 | 雾霾天气的主要成因 | 百分比 |
| A | 工业污染 | 45% |
| B | 汽车尾气排放 | |
| C | 生活炉烟气排放 | 15% |
| D | 其他(滥砍滥伐等) |
(2)若该市有100万人口,请估计持有A、B两类看法的市民共有多少人?