Question

Select the statement that is true. Group of answer choices There are integers s and t such that 2=102⋅s+72⋅t . here are integers s and t such that 8=102⋅s+72⋅t . There are integers s and t such that 1=102⋅s+72⋅t . There are integers s and t such that 6=102⋅s+72⋅t .

Answer 1

The statement that is true is: There are integers s and t such that 2=102⋅s+72⋅t.

Step-by-step explanation:

The statement that is true is:

There are integers s and t such that 2=102⋅s+72⋅t.

To determine if this statement is true, we can try to find values of s and t that satisfy the equation. Let's rearrange the equation:

2 = 102⋅s + 72⋅t

2 = 6⋅(17⋅s + 12⋅t)

Since 6 is a factor of 2, there exist integers s and t that satisfy the equation. For example, s = 1 and t = -1 would make the equation true: 2 = 6⋅(17⋅1 + 12⋅(-1))