10类NCERT解决方案-第3章两个变量的线性方程对–练习3.1

问题1. Aftab告诉他的女儿：“七年前，我的年龄是当时的7倍。而且，从现在开始的三年后，我的年龄将是您的三倍。” (这不是很有趣吗?)用数字和图形方式表示这种情况。

解决方案：

Present age of Aftab = x

And, the present age of his daughter = y

Seven years ago,

Age of Aftab = x-7

Age of his daughter = y-7

Three years after,

Age of Aftab = x+3

Age of his daughter = y+7

Here, According to the given condition,

x−7 = 7(y−7)

x−7 = 7y−49

x−7y = −42         ………………………(I)

To draw the line for Eqn. (I), we need at least two solutions of the equation, So, we can use the following table to draw the graph:

x	y
0	6
-42	0

And, According to the another given condition,

x+3 = 3(y+3)

x+3 = 3y+9

x−3y = 6       …………..…………………(II)

To draw the line for Eqn. (II), we need at least two solutions of the equation, So, we can use the following table to draw the graph:

x	y
0	-2
6	0

The graphical representation of Eqn. (I) and Eqn. (II) is:

问题2.板球队的教练以3900卢比的价格购买了3个球拍和6个球。后来，她以1300卢比的价格购买了另外一个球拍和3个相同种类的球。用代数和几何方式表示这种情况。

解决方案：

The cost of a bat = ₹ x

And, the cost of a ball = ₹ y

Here, According to the Given condition,

3x+6y = 3900 …………………….(I)

x+3y = 1300 …………………….(II)

To draw the line for Eqn. (I), we need at least two solutions of the equation, So, we can use the following table to draw the graph:

x	y
0	650
1300	0

To draw the line for Eqn. (II), we need at least two solutions of the equation, So, we can use the following table to draw the graph:

x	y
100	400
1300	0

The graphical representation of Eqn. (I) and Eqn. (II) is:

问题3.每天2公斤苹果和1公斤葡萄的成本为₹160。一个月后，4公斤苹果和2公斤葡萄的成本为300卢比。用代数和几何方式表示情况。

解决方案：

The cost of 1 kg of apples = ₹ x

And, cost of 1 kg of grapes = ₹ y

Here, According to the given conditions,

2x+y = 160 ………………………(I)

4x+2y = 300 ………………………(II)

To draw the line for Eqn. (I), we need at least two solutions of the equation, So, we can use the following table to draw the graph:

x	y
0	160
80	0

To draw the line for Eqn. (II), we need at least two solutions of the equation, So, we can use the following table to draw the graph:

x	y
0	150
75	0

The graphical representation of Eqn. (I) and Eqn. (II) is: