CBSE Class 10-Mathematics: Chapter –3 Pair of Linear Equation in Two Variables Part 8

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Question 4:

One says, “Give me a hundred, friend! I shall then become twice as rich as you.” The other replies, “If you give me ten, I shall be six times as rich as you.” Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II]

Answer:

Let the money with the first person and second person be Rs and Rs respectively.According to the question,

Again,

Multiplying equation (2) by , we obtain:Subtracting equation from equation , we obtain:

Putting the value of x in equation (1), we obtain:

Thus, the two friends had Rsand Rs with them.

Question 5:

The students of a class are made to stand in rows. If students are extra in a row, there would be 1 row less. If students are less in a row, there would be rows more. Find the number of students in the class.

Answer:

Let the number of rows be x and number of students in a row be y.Total number of students in the class Number of rows Number of students in a row

According to the question,

Total number of students

Subtracting equation (2) from (1), we obtain:

Substituting the value of y in equation (1), we obtain:

Number of rows

Number of students in a row

Hence,

Total number of students in a class

Question 6:

Find the values of for which the following system of linear equations has infinite number of solutions,

Answer:

Question 7:

Find the condition for which the system of equations and is inconsistent.

Answer:

In consistent