Q2 of 92 Page 58

Let us form the simultaneous equations in each of the following cases and see whether the solution of them is possible or not.

Mita has 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 Rs. 126.


(a) Let me draw the graph after forming the simultaneous equations.


(b) With the help of graph, let me find whether the general solution of two equations can be determined.


(c) Let me write the price of 1 pen and 1 pencil separately from the graph.

Let’s take the value of pen = Rs X


Value of pencil = Rs Y


Given that


Mita has bought 3 pens and 4 pencils for Rs.42


So we can write the equation as


3(PEN) +4(PENCIL) =42


3X + 4Y =42 ……… (1)


Also given that


I bought 9 pens and 1 dozen pencils at the same rate to give gifts to my friends at the Rs. 126.


Equation become


9X+12Y =126 ……… (2)


If we divide both sides by 3 we get


3X +4Y = 42


Both equation (1) and (2) are the same, so there exist an infinite number of solutions.


We can plot this equation, see the figure given below -



Every point laying on this line on 1st quadrant can be our answer …


So there is an infinite number of solution to this question.


More from this chapter

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1

Let us form the simultaneous equations in each of the following cases and see whether the solution of them is possible or not.

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 of my sister’s age.


(a) Let me draw the graph after framing simultaneous equations.


(b) With the help of graph, let me find out whether the general solution of two equations can be determined.


(c) Let me write the present age of my elder sister and father from the graph.

 3

Let us form the simultaneous equations in each of the following cases and see whether the solution of them is possible or not.

Today we shall draw the pictures as we like in our school. For this, I have bought 2 art papers and 5 sketch pens at Rs.16. But Dola has bought 4 art papers and 10 sketch pens of the same rate and from the same shop.


(a) Let me form simultaneous equations and draw the graph.


(b) Let me see whether the general solution of the equations can be found out from the graph.


(c) Let me write whether I can get the price of 1 art paper and 1 sketch pen.

 1

Let us draw the graph of the following simultaneous equations and write whether they are solvable or not and if they are solvable, let us write that particular solution or 3 solutions if they have infinite number of solutions:

2x + 3y – 7 = 0


3x + 2y – 8 = 0

 1

Let us draw the graph of the following simultaneous equations and write whether they are solvable or not and if they are solvable, let us write that particular solution or 3 solutions if they have infinite number of solutions:

4x – y = 0


–8x + 2y = –22