abed says he has written a system of two linear equations that has an infinite number of solutions. one of…

Explanation:

Step1: Recall condition for infinite - solutions

A system of two linear equations (y = mx + b) and (y=m_1x + b_1) (or (Ax+By = C) and (A_1x + B_1y=C_1)) has infinite solutions when the two equations represent the same line, i.e., they have the same slope (m=m_1) and the same y - intercept (b = b_1) (or are scalar multiples of each other in standard form (Ax+By = C)). The given equation is (y = 3x-1), which can be rewritten as (3x - y=1) in standard form (Ax + By=C).

Step2: Check each option

• Option 1: (y = 3x + 2) has the same slope (m = 3) but different y - intercept ((b=-1) for (y = 3x-1) and (b = 2) for (y = 3x + 2)), so it is not the same line.
• Option 2: (3x-y=2) is not a scalar - multiple of (3x - y=1).
• Option 3: (3x - y=1) is the same as the given equation (y = 3x-1) when rewritten in standard form, so the two equations represent the same line.
• Option 4: (3x + y=1) is not a scalar - multiple of (3x - y=1).

Answer:

C. (3x - y = 1)