Multiple choice

Solve the following pairs of equations. $x-2y=6$; $x-2y=-6$

  1. No solution

  2. Infinite solution

  3. Unique solution

  4. None of these
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A Correct answer
Explanation

The equations are x - 2y = 6 and x - 2y = -6. Since the left sides are identical but the constants are different, the lines are parallel and never intersect, meaning there is no solution.

AI explanation

Comparing the coefficients of the given equations x - 2y = 6 and x - 2y = -6, the ratios of x and y are 1/1 = 1 and (-2)/(-2) = 1. However, the ratio of the constant terms is 6/(-6) = -1. Because the ratio of the coefficients is not equal to the ratio of the constants, the lines are parallel, meaning the system has no solution.

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