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Written with integer coefficients in the form ax + by + , the equation becomes:

Class 9Linear Equations in Two VariablesLinear Equations
  • A
  • B
  • C
  • D

Step-by-Step Solution

Multiply every term by 6: , so . Check with (2, 0): 2/2 + 0 = 1 ✓ and ✓. Dividing by 2 produces the coefficient 3, so do not swap a and b.
Answer: D)

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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