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 $y = m_1x + b_1$ and $y=m_2x + b_2$ has infinite solutions when $m_1=m_2$ and $b_1 = b_2$, or when the two equations are equivalent. Rewrite the given equation $y = 3x-1$ in standard form $Ax + By=C$, we get $3x - y=1$.

Step2: Check each option

• Option 1: $y = 3x + 2$ has the same slope ($m = 3$) but different y - intercept, so it is parallel to $y = 3x-1$ and the system has no solutions.
• Option 2: Rewrite $3x - y=2$ as $y = 3x - 2$, different from $y = 3x-1$, so the system has no solutions.
• Option 3: Rewrite $3x - y=1$ as $y = 3x - 1$, which is equivalent to the given equation $y = 3x-1$, so the system has infinite solutions.
• Option 4: Rewrite $3x + y=1$ as $y=-3x + 1$, different slope, so the system has one solution.

Answer:

$3x - y = 1$