To determine which equations are in standard form, we need to recall that the standard form of a linear equation in two variables is generally written as:
\[ Ax + By = C \]
where \( A \), \( B \), and \( C \) are integers, and \( A \) should be non-negative.
Let's go through the given options:
-
\( x + 0.25y = 4 \)
This is not in standard form because \( 0.25 \) is not an integer; it should be an integer in standard form. -
\( x + 2y = 12 \)
This is in standard form: \( A = 1 \), \( B = 2 \), and \( C = 12 \) (and A is non-negative). -
\( -x + y = 5 \)
This is technically in standard form, but it has a negative coefficient for \( x \). In standard form, we typically prefer \( A \) to be non-negative, so it can also be rewritten to \( x - y = -5 \) if we choose to convert it. However, it can still be considered to be in standard form depending on the definition being followed.
Considering these points, the two equations that fit the definition of standard form are:
- \( x + 2y = 12 \)
- \( -x + y = 5 \) (though typically we avoid negative A)
Therefore, the equation \( x + 2y = 12 \) is the clearest example of an equation in standard form.