Final answer:
The correct system of equations that represents 6x - 8 = 4 is option 3) y = 6x - 8 and y = -4, where the first equation represents the linear relationship and the second is the constant value of y.
Step-by-step explanation:
The student is asking to find the system of equations that represents the given equation 6x – 8 = 4. This can be turned into a linear equation by isolating y on one side, which gives us y = 6x – 8. A system of equations involves more than one equation, and since 6x - 8 = 4 is equivalent to y = 6x – 12, the first equation in our system is y = 6x - 8. To find a second equation, we should look to equate y to a constant since no other variables are given. The given equation 6x - 8 = 4 simplifies to y = -4 when turned into a y-based equation, as the constant term on the right-hand side of the equation should be what y equals when x is zero. Therefore, the correct system of equations is y = 6x – 8 and y = –4, making option 3) the correct choice.