Question

analyzing a system of equations with infinitely many solutions
abed says he has written a system of two linear equations that has an infinite number of solutions. one of the equations of the system is $y = 3x - 1$. which could be the other equation?
$\circ$ $y = 3x + 2$
$\circ$ $3x - y = 2$
$\circ$ $3x - y = 1$
$\circ$ $3x + y = 1$

Explanation:

Step1: Recall infinite solutions condition

A system of two linear equations has infinitely many solutions if the equations are equivalent (one is a scalar multiple of the other, representing the same line).

Step2: Rewrite given equation

Start with the given equation $y = 3x - 1$. Rearrange it to standard form:
$$3x - y = 1$$

Step3: Match with options

Compare the rearranged equation to the options. The equation $3x - y = 1$ is identical to the third option, meaning it is the same line as the original equation.

Answer:

$3x - y = 1$