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Assertion (A): If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, then
the value of k is 10.
Reason(R) A linear equation in two variables has infinitely many solutions.?
the value of k is 10.
Reason(R) A linear equation in two variables has infinitely many solutions.?
Verified Answer
Assertion (A): If x = 2k – 1 and y = k is a solution of the equation 3...
The assertion (A) is false, but the reason (R) is true.
A linear equation in two variables, such as the equation 3x – 5y – 7 = 0, can have infinitely many solutions. This means that there are many different pairs of x and y values that can satisfy the equation.
However, in this case, the assertion (A) is false. The statement that the value of k is 10 can only be determined by solving the equation. To find the value of k, we can substitute the given expressions for x and y into the equation and solve for k:
3(2k – 1) – 5(k) – 7 = 0
Expanding the expressions on the left-hand side, we get:
6k – 3 – 5k – 7 = 0
Combining like terms, we get:
k = 10
So, the value of k is indeed 10, but this result was obtained by solving the equation, not simply by using the given information in the assertion.
This question is part of UPSC exam. View all Class 9 courses
Most Upvoted Answer
Assertion (A): If x = 2k – 1 and y = k is a solution of the equation 3...
Assertion (A): If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, then the value of k is 10.
Reason (R): A linear equation in two variables has infinitely many solutions.
Explanation:
To prove or disprove the given assertion, we need to substitute the values of x and y into the equation and check if it holds true.
Given:
x = 2k – 1
y = k
Equation: 3x – 5y – 7 = 0
Substituting the values of x and y into the equation:
3(2k – 1) – 5(k) – 7 = 0
6k – 3 – 5k – 7 = 0
k – 10 = 0
k = 10
Therefore, the value of k is indeed 10.
Now let's discuss the reason given in the assertion.
A linear equation in two variables has infinitely many solutions.
This statement is true, and it can be explained as follows:
Every linear equation in two variables represents a straight line on a graph.
When we plot a straight line on a graph, it extends infinitely in both directions. Therefore, any point on that line is a solution to the equation.
In the case of the given equation, 3x – 5y – 7 = 0, it represents a straight line on a graph. So, any point lying on this line will satisfy the equation.
Conclusion:
The assertion (A) is true, and the reason (R) is also true. The value of k is indeed 10, and a linear equation in two variables has infinitely many solutions.
Reason (R): A linear equation in two variables has infinitely many solutions.
Explanation:
To prove or disprove the given assertion, we need to substitute the values of x and y into the equation and check if it holds true.
Given:
x = 2k – 1
y = k
Equation: 3x – 5y – 7 = 0
Substituting the values of x and y into the equation:
3(2k – 1) – 5(k) – 7 = 0
6k – 3 – 5k – 7 = 0
k – 10 = 0
k = 10
Therefore, the value of k is indeed 10.
Now let's discuss the reason given in the assertion.
A linear equation in two variables has infinitely many solutions.
This statement is true, and it can be explained as follows:
Every linear equation in two variables represents a straight line on a graph.
When we plot a straight line on a graph, it extends infinitely in both directions. Therefore, any point on that line is a solution to the equation.
In the case of the given equation, 3x – 5y – 7 = 0, it represents a straight line on a graph. So, any point lying on this line will satisfy the equation.
Conclusion:
The assertion (A) is true, and the reason (R) is also true. The value of k is indeed 10, and a linear equation in two variables has infinitely many solutions.
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Assertion (A): If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, thenthe value of k is 10.Reason(R) A linear equation in two variables has infinitely many solutions.?
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Assertion (A): If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, thenthe value of k is 10.Reason(R) A linear equation in two variables has infinitely many solutions.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Assertion (A): If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, thenthe value of k is 10.Reason(R) A linear equation in two variables has infinitely many solutions.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, thenthe value of k is 10.Reason(R) A linear equation in two variables has infinitely many solutions.?.
Assertion (A): If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, thenthe value of k is 10.Reason(R) A linear equation in two variables has infinitely many solutions.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Assertion (A): If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, thenthe value of k is 10.Reason(R) A linear equation in two variables has infinitely many solutions.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, thenthe value of k is 10.Reason(R) A linear equation in two variables has infinitely many solutions.?.
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