Final answer:
Standard form of a linear equation is typically Ax + By = C with A, B, and C as integers. Equations 2x + 3y = –6 and –4x + 3y = 12 are in standard form, along with 5x + 3y = 5 if fractions are allowed. The equation x - y = 5 is also in standard form.
Step-by-step explanation:
In mathematics, standard form for a linear equation is often written as Ax + By = C, where A, B, and C are integers, and A should be a non-negative integer. Given a list of equations, we can determine which ones fit the definition of standard form.
The equations 2x + 3y = –6 and –4x + 3y = 12 are already in standard form because they meet the Ax + By = C criteria with A, B, and C being integers. However, the equation 5x + 3y = 5 also can be considered in standard form even though it contains fractions; the form is maintained.
Equations like y = 2x + 5 and y = ½x + 3 are not in standard form because they do not match the Ax + By = C format; they are in slope-intercept form y = mx + b.
The equation x - y = 5 is in standard form, as it can be rearranged to -y + x = 5 (or x - y = 5 in its more common arrangement) and it fits the standard form criteria even though A is negative, which can be acceptable depending on the convention followed.