Final answer:
The second equation that would make the system have no solution is 4x + 2y = 6, because it has the same slope as the first equation but a different y-intercept.
Step-by-step explanation:
In a system of linear equations, having no solution means that the two lines represented by the equations are parallel. The first equation given is 4x + 2y = –8. To be parallel, the second equation must have the same slope but a different y-intercept. To find the slope of the first equation, we can put it into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:
2y = -4x - 8
y = (-4x - 8)/2
y = -2x - 4
The slope of the first equation is -2. Examining the options, the equation 4x + 2y = 6 has the same left-hand side as the first equation, thus it would also have a slope of -2 after division by 2. Since it has a different y-intercept, this is the equation that would make the system have no solution.