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Meena plots the graph of . She marks six points with whole-number coordinates on it, and then point M at (2.5, 1.5), which also fits. What does this show about the solutions of ?

Class 9Linear Equations in Two VariablesLinear Equations
  • AIt has exactly 6 solutions
  • BIt has exactly 7 solutions
  • CIt has infinitely many solutions
  • DIt has only one solution

Step-by-Step Solution

Every point on the line is a solution, including points with fractional coordinates like . A line has infinitely many points, so has infinitely many solutions.
Answer: C) It has infinitely many solutions

Key idea: Finding solutions to a linear equation

Pick any value for one variable; solve for the other. Repeat to get many solutions.

Example: .
- Let → . So (0, 6) is a solution (this is the -intercept).
- Let → . So (2, 3) is a solution.
- Let → . So (4, 0) is a solution (this is the -intercept).
- Let → . Same as above.

Four solutions found in seconds, and infinitely more available.

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