How many linear equation in x and y can be satisfied by x = 1 and y = 2?
Chapter 4: Linear Equations in Two Variables is an essential part of Class 9th Mathematics. This NCERT solution guide provides accurate answers to MCQ-based and short-answer questions, helping students grasp key concepts effortlessly. It explains different methods like substitution, elimination and graphical representation in a simple, step-by-step manner. Designed to enhance problem-solving skills, this resource is perfect for exam preparation and building a strong mathematical foundation. With clear explanations and structured solutions, students can improve their understanding and confidently approach linear equation problems.
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To determine how many linear equations in x and y can be satisfied by x=1 and y=2, let’s analyze the situation.
A linear equation in x and y typically has the form: Ax+By=C
where A, B and C are constants. For a given pair ( x = 1, y= 2), we can substitute these values into the equation to see if it holds.
Step 1: Substitute x=1 and y=2 into the general form of the equation Ax + By = C:
A(1) + B(2) = C
A + 2B = C
This equation can be true from many different values of A, B and C. So, there is not just one equation, but many possible equations that can be formed depending on the values of A and B.
Step 2: General conclusion
There is no unique solution for the values of A, B and C. This means infinitely many linear equations can be satisfied by the point (x=1,y=2).
Conclusion:
The correct answer is (c) infinitely many.
This question related to Chapter 4 Mathematics Class 9th NCERT. From the Chapter 4 Linear Equation in Two Variables. Give answer according to your understanding.
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