Maths WBBSE Class 9 Solutions Chapter 5 Linear Simultaneous Equations Exercise 5.1
Let me frame the simultaneous equations in each of the following cases and see whether they can be solved or not.
Question 1. The sum of my elder sister’s present age and my father’s present age is 55 years. By calculating, I observed that after 16 years, my father’s age will be two times more than my sister’s.
1. Let me draw the graph after framing simultaneous equations.
2. With the help of a graph, let me find out whether the general solution of two equations can be determined.
3. Let me write the present age of my elder sister and father from the graph.
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Solutions:
Given
The sum of my elder sister’s present age and my father’s present age is 55 years. By calculating, I observed that after 16 years, my father’s age will be two times more than my sister’s.
Let the elder sister’s present age x years and the father’s present age be y years.
According to the conditions,
x + y = 55……(1)
2(x+16) = y + 16 …(2)
From equation…(1)
→AB
| x | 25 | 35 | 40 |
| y | 30 | 20 | 15 |
From equation …(2)
2x-y = -16
→CD
| x | -5 | 0 | -8 |
| y | 6 | 16 | 0 |
General solution x = 13, 4 = 42
∴ The present age of sister (x) = 13 years and the present age of father (y) = 42 years.
Question 2. Mita bought 3 pens and 4 pencils at Rs. 42 from the shop of Jadabkaku. I bought 9 pens and 1 dozen pencils at the same rate to give gifts to my friends at the cost of Rs. 126.
1. Let me draw the graph after forming the simultaneous equations.
2. With the help of a graph, let me find whether the general solution of two equations can be determined.
3. Let me write the price of 1 pen and 1 pencil separately from the graph. Ans. Let the cost price of one pen = Rs. x and the cost price of one pencil = Rs. y.
Solution:
Given
Mita bought 3 pens and 4 pencils at Rs. 42 from the shop of Jadabkaku. I bought 9 pens and 1 dozen pencils at the same rate to give gifts to my friends at the cost of Rs. 126.
∴ Required simultaneous equations are
3x + 4y = 42…..(1)
9x+12y= 126…(2)
From equation ….(1)
3x + 4y = 42
or, \(x=\frac{42-4 y}{3}\)
→AB
| x | 14 | 10 | 6 |
| y | 0 | 3 | 6 |
From equation…………. (2)
9x=126-12y
or, \(x=\frac{126-12 y}{9}\)
→CD
| x | 10 | 14 | 6 |
| y | 3 | 0 | 6 |
Class IX Maths Solutions WBBSE
2. Infinite number of general solutions x = 10, y = 3 or, x = 6, y = 6
3. price of 1 pen = Rs. 10 & price of 1 pencil = Rs. 3
or, price of 1. pen = Rs. 6 & price of 1 pen = Rs. 6.
Question 3. Today we shall draw the pictures as we like in our school. For this, I bought 2 art paper and 5 sketch pens at Rs. 16. But Dola has bought 4 art paper and 10 sketch pens of the same rate and from the same shop.
1. Let me form simultaneous equations and draw the graph.
2. Let me see whether the general solution of the equations can be found out from the graph.
3. Let me write whether I can get the price of 1 art paper and 1 sketch pen.
Solution:
Given
Today we shall draw the pictures as we like in our school. For this, I bought 2 art paper and 5 sketch pens at Rs. 16. But Dola has bought 4 art paper and 10 sketch pens of the same rate and from the same shop.
Let the price of art paper = Rs. x & that of one sketch pen = Rs. y.
Class IX Maths Solutions WBBSE
∴ Required equations,
2x+5y= 16
From equation….(2)
4x + 10y = 28
or, x = \(x=\frac{28-10 y}{4}\)
2. will have no general solutions
3. No definite value of one art paper & one sketch pen.
