To determine which of the given equations is in standard form, we need to recall that the standard form of a linear equation in two variables is typically written as:
\[ Ax + By = C \]
where \( A \), \( B \), and \( C \) are integers, and \( A \) should be a non-negative integer.
Let's analyze each of the equations given:
-
\( x + y = 7.5 \)
This equation is not in standard form because the right side (7.5) is not an integer. -
None of these are in standard form.
This option requires us to evaluate the others first. -
\( x - y = -7 \)
This equation can be rewritten as \( 1x - 1y = -7 \). Here, \( A = 1 \), \( B = -1 \), and \( C = -7 \). Although it contains negative coefficients, it is still in the form \( Ax + By = C\) (but \( A \) should ideally be non-negative). -
\( 0.1x + 0.25y = 7 \)
This equation is not in standard form due to the coefficients \( 0.1 \) and \( 0.25\) being decimals. If converted to standard form, we would typically multiply through by 100 to eliminate the decimals, leading to \( 10x + 25y = 700 \), which would then be in standard form.
Given this analysis, the equation \( x - y = -7 \) is the closest to standard form, even if it doesn't strictly adhere to the conventional requirement for \( A \) being non-negative. Therefore, the best answer from the provided options is:
\( x - y = -7 \)