If x and y are negative, which of the following show a positive x and y?
Answer (1)
To determine if both x and y can be positive numbers given the condition that both x and y are initially negative, we need to consider the rules of multiplication and the number line.
Understanding Negative Numbers: Negative numbers are numbers less than zero. On a number line, they are to the left of zero. Both x and y are negative, so without any additional transformation or operation, they cannot both become positive by themselves.
Multiplication Facts: If two negative numbers are multiplied together, the result is a positive number. This is due to the rule that states 'a negative times a negative is a positive'. However, this will not change the individual signs of x and y, only their product.
Transformation to Positive Numbers: To make x and y themselves positive, you would typically need to add a positive number larger than the absolute value of x and y to each, or multiply each by -1.
Example: If x = -3 and y = -2, to make them both positive, you can add values large enough to offset the negativity and go beyond zero. For instance, adding 4 to x gives -3 + 4 = 1 (positive), and adding 3 to y gives -2 + 3 = 1 (positive).
Therefore, in the context of a multiple-choice question asking which option can result in positive x and y, such options are usually transformations or operations that change the signs, such as multiplying both by -1 or some contextually relevant condition based on equational transformations.
