Multiple choice

Solve the equation: $x - 36y = 8$ and $\dfrac{-1}{6}x + 6y = -48$ and then identify the system of equation.

  1. Consistent

  2. Inconsistent

  3. Dependent

  4. All the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The second equation is -1/6x + 6y = -48. Multiply by -6 to get x - 36y = 288. The first equation is x - 36y = 8. Since 8 is not equal to 288, the lines are parallel and the system is inconsistent.

AI explanation

To determine consistency, compare the ratio of the coefficients of x, y, and the constants for both equations. For x - 36y = 8 and (-1/6)x + 6y = -48, the ratios of the coefficients are 1/(-1/6) = -6 and -36/6 = -6. Since the ratio of the coefficients is equal but differs from the ratio of the constants, 8/(-48) = -1/6, the lines are parallel. Therefore, the system of equations is inconsistent and has no solution.

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