Final answer:
The linear equation -3x + 4y = 12 has infinitely many solutions since it represents a line, and the arithmetic statement one-fourth minus one-third equals 1 is false and has no solution. Therefore, the equations are not related to each other.
Step-by-step explanation:
The question asks whether the equations -3x + 4y = 12 and one-fourth minus one-third equals 1 have a solution, and if so, what type of solution. To determine this, we analyze each statement separately.
First, let's deal with the linear equation -3x + 4y = 12. This is a standard form linear equation and represents a line on a graph. It can have many points (x, y) that satisfy it, but each x corresponds to exactly one y, given that it is not a vertical or horizontal line. Each x-y pair is a solution to the equation. Since it is a line, it will have infinitely many solutions as long as we're dealing with real numbers.
Now, for the arithmetic equation one-fourth minus one-third equals 1, this is simply incorrect. Mathematically:
¼ - ⅓ ≠ 1
¼ - ⅓ = -⅜
Therefore, the arithmetic equation has no solution because the statement is false.
Considering both parts of the question, the correct statement is that the equations are not related to each other (choice 4).