Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

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Study for the ALEKS Exam with in-depth coverage. Utilize flashcards and multiple-choice questions with hints and explanations to get prepared!

Each practice test/flash card set has 50 randomly selected questions from a bank of over 500. You'll get a new set of questions each time!

Practice this question and more.

In the equation Ax + By = C, what do A and B need to fulfill?

Must be equal to zero
Both must be negative
Cannot both be zero
Must be whole numbers

The correct answer is: Cannot both be zero

In the equation Ax + By = C, A and B serve as the coefficients that determine the slope and position of the line represented by the equation in a two-dimensional Cartesian coordinate system. For the equation to represent a valid line, the conditions related to A and B must ensure that the line has a defined slope. The requirement that A and B cannot both be zero is crucial because if both coefficients were zero, the equation would simplify to 0 = C. If C is not zero, this would represent an inconsistency (no solutions), and if C equals zero, it would imply that any x and y values would have to satisfy 0 = 0, leading to an indeterminate situation rather than a specific line. Thus, at least one of the coefficients must be non-zero to maintain the integrity of the linear equation, allowing it to signify a unique line in the coordinate plane. The other options suggest conditions about the values of A and B that are not necessary for the equation to hold. For example, A and B do not need to be equal to zero or both negative, nor do they need to be whole numbers, as the coefficients can be any real numbers, providing a wider range of possibilities for the equation.