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
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
Or