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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The solution of a linear equation in two variables is an ordered pair (x,y) that satisfies the equation when the values of x and y are substituted into the equation.
Explanation:
A linear equation in two variables typically has the form ax+by=c, where a, b, and c are constants, and x and y are the variables. The solution is the set of values x and y (an ordered pair) that, when substituted into the equation, make the equation true.
Option (a): a number which satisfies the given equation
This is not correct because the solution is not just a single number but an ordered pair of numbers. So, (a) is incorrect.
Option (b): an ordered pair which satisfies the given equation
This is partially correct, but it’s a bit incomplete because it doesn’t clarify that the ordered pair is specific to the equation and needs to satisfy the equation. (b) is incomplete.
Option (c): an ordered pair, whose respective values when substituted for x and y in the given equation, satisfies it
This is the most accurate description. The solution is indeed an ordered pair, and when the values of x and y are substituted into the equation, the equation must be satisfied. (c) is correct.
Option (d): none of these
Since option (c) is correct, this option is incorrect. (d) is incorrect.
Conclusion: The correct answer is (c) an ordered pair, whose respective values when substituted for x and y in the given equation, satisfies it.
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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https://www.tiwariacademy.in/ncert-solutions/class-9/maths/

The point of the form (a,−a) represents a point where the x-coordinate is aaa and the y-coordinate is −a.
Step 1: Let’s check each option:
Option (a): x=a
For the point (a,−a) the x-coordinate is a. So, x=a is true. However, the equation x=a does not necessarily describe the relationship between x and y because the y-coordinate −a, not a. Therefore, (a) is incorrect.
Option (b): y=−a
The point (a, -a) has a y-coordinate of -a. This satisfies y = -a, but it doesn’t describe the relation between x and y in general, because it does not account for both coordinates. (b) is incorrect.
Option (c): y = x
For the point (a, -a), the y – coordinate is -a, not a. Therefore, y = x does not hold true for the point. (c) is incorrect.
Option(d): x + y = 0
For the point (a, -a), if we add the coordinates, we get: x + y = a + (-a) = 0
This is true! The point (a, -a) always satisfies the equation x + y = 0.
Conclusion:
The correct answer is (d) x+y=0x + y = 0x+y=0.
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.

For more please visit here:
https://www.tiwariacademy.in/ncert-solutions/class-9/maths/