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Assertion (A): The point (0, 0) is a solution of . Reason (R): A line of the form ax + by = 0 always passes through the origin. Which is correct?

Class 9Linear Equations in Two VariablesLinear Equations
  • ABoth A and R are true, and R correctly explains A
  • BBoth A and R are true, but R does not explain A
  • CA is true, R is false
  • DA is false, R is true

Step-by-Step Solution

2(0)+3(0)=0 so (0,0) is a solution (A true). Any equation ax+by=0 has no constant term, so (0,0) satisfies it (R true), and that is exactly why A holds.
Answer: A) Both A and R are true, and R correctly explains A

Key idea: Lines parallel to the axes

Two special cases:

** = constant**: a horizontal line (parallel to -axis). Example: is the line of all points with ordinate 4. Every solution has regardless of = constant**: a vertical line (parallel to -axis). Example: is the line of all points with abscissa −2.

Algebraically: is ; is . They fit the standard form ax + by + with one of a, b being 0.

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