代数-方程组

代数-方程组
2015-11-21 flyfish 笔记
方程组（system of equations）：把若干个方程合在一起研究，使其中的未知量同时满足每一个方程的一组方程。

一
The square of x is equal to 9 times the square of y. If x is 1 more than 3 timesy，what is the value of x？

x^2=9(y^2)
x=1+3y

二
Each student in a group of 30 students studies Italian，Spanish，or both. The total number of students studying Italian is three more than the total number of students studying Spanish. If the number of students that study both subjects is the same as the number of students that study exactly one subject，how many students in the group study only Italian？

设
学习Italian的人 Italian=x
学习Spanish的人 Spanish=x-3
两样都学习的人 both=y

只学习Italian的人 x-y
只学习Spanish的人 x-3-y

2y=30
(x-y)+(x-3-y)=y
解得
y=15,x=24

三
One number is 8 more than twice another number. If the sum of the two numbers is 23，what is the smaller of the two numbers？

one number= x
another nnuber=y

x=8+2y
x+y=23