线性方程

练习4.1

问题1:笔记本的价格是钢笔的两倍。写一个双变量线性方程来表示上面的表述。

答:假设一个笔记本的成本是x，一支钢笔的成本是y。
根据问题，
一本笔记本的价格是一支钢笔的两倍
或者x = 2y
或者x - 2y = 0。

问题2:将下列线性方程以ax + by + c = 0的形式表示，并分别表示a、b和c的值:

(i) 2x + 3y = 9.35
(ii) x- (y/5) - 10 = 0
(iii) -2x + 3y = 6
(iv) x = 3y
(v) 2x = -5y
(vi) 3x + 2 = 0
(vii) y - 2 = 0
(viii) 5 = 2x

解决方案:(i) a = 2, b = 3, c = 9.35

(ii) a = 1, b =(-1/5)和c = -10

(iii) -2x + 3y = 6

或者-2x + 3y - 6 = 0
将方程与ax + by + c = 0进行比较，我们有
A = -2, b = 3, c = -6

(iv) x = 3y

或者x - 3y = 0
将方程与ax + by + c = 0进行比较，我们有
A = 1, b = -3, c = 0

(v) 2x = -5y

或者2x + 5y = 0
将方程与ax + by + c = 0进行比较，我们有
A = 2, b = 5, c = 0

(vi) 3x + 2 = 0

3x + 0y + 2 = 0
将方程与ax + by + c = 0进行比较，我们有
A = 3 b = 0 c = 2

(vii) y - 2 = 0

或者，0x + 1y - 2 = 0
将方程与ax + by + c = 0进行比较，我们有
A = 0, b = 1, c = -2

(viii) 5 = 2x

或者-2x - 0y + 5 = 0
将方程与ax + by + c = 0进行比较，我们有
A = -2, b = 0, c = 5