Final answer:
Upon comparing each pair of equations, it becomes clear that equations D (x - 9y = 24) and H (y = 4 - 2x) produce infinitely many solutions as they are identical; they represent the same line when rearranged into slope-intercept form.
Step-by-step explanation:
To determine which system will produce infinitely many solutions, we need to identify pairs of equations that are actually the same line, meaning they have the same slope and y-intercept. Starting with equations in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept, is an efficient way to do this.
We can rearrange the equations into the slope-intercept form if they are not already in that form. For instance, equation B is already in the form with a slope of -4 and y-intercept of -10. Taking equation F for comparison, if we rearrange it we get y = -1/3 x + 5/3, which has a different slope and y-intercept than equation B. Thus, B and F are not identical.
Now, comparing equation E and equation B, rearranging E gives us y = 1/4x + 9/4, which has a different slope and y-intercept from B.
Finally, comparing equation H with others, we see that rearranging gives us y = -1/2x + 4, which has a slope of -1/2 and y-intercept of 4. This matches the slope and y-intercept of equation D exactly when that is also rearranged (y = -1/2x + 12). Therefore, equations D and H are identical, representing the same line, and will produce infinitely many solutions.