Multiple choice

Check whether the pair of equations $x + 3y = 6$, and $2x - 3y = 12$ is consistent. If so, solve graphically

  1. Yes; $x=6, y=0$
  2. No; $x=6, y=0$

  3. Ambiguous

  4. Data insufficient
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A Correct answer
Explanation

x + 3y = 6 and 2x - 3y = 12. Adding them: 3x = 18 => x = 6. Substituting: 6 + 3y = 6 => y = 0. Since there is a unique solution, the system is consistent.

AI explanation

Add the two simultaneous equations (x + 3y = 6) and (2x - 3y = 12) to eliminate y. This yields 3x = 18, meaning x = 6. Substituting x = 6 into the first equation gives 6 + 3y = 6, which simplifies to y = 0. The system is consistent, and the solution is x = 6 and y = 0.

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