Assertion (A): A linear equation 2x + 3y = 5 has a unique solution.Reason (R): A linear equation in two variables has infinitely many solutions
Question
Assertion (A): A linear equation 2x + 3y = 5 has a unique solution.Reason (R): A linear equation in two variables has infinitely many solutions
Solution
The assertion (A) and the reason (R) are both correct, but the reason (R) does not correctly explain the assertion (A).
Here's why:
Assertion (A): A linear equation 2x + 3y = 5 does indeed have a unique solution. This is because it is a linear equation in two variables, and any such equation represents a straight line in a two-dimensional space. Any point on this line is a solution to the equation. However, the equation 2x + 3y = 5 represents a specific line, and there is only one such line that satisfies this equation. Therefore, the assertion is correct.
Reason (R): A linear equation in two variables does indeed have infinitely many solutions. This is because any such equation represents a straight line in a two-dimensional space, and any point on this line is a solution to the equation. Therefore, there are infinitely many points on the line, and hence, infinitely many solutions to the equation. So, the reason is also correct.
However, the reason (R) does not correctly explain the assertion (A). The assertion (A) is talking about a specific linear equation (2x + 3y = 5), while the reason (R) is talking about linear equations in two variables in general. The fact that linear equations in two variables have infinitely many solutions does not explain why the specific equation 2x + 3y = 5 has a unique solution (i.e., why it represents a unique line). Therefore, while both the assertion and the reason are correct, the reason does not correctly explain the assertion.
Similar Questions
Assertion (A): There are infinite number of lines which pass through (2, 14)Reason(R): A linear equation in two variables has infinitely many solutions
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