For what ordered pair (a, b) are there infinite solutions (x, y) to the system
I dont think such values exist.
We can simplify the equations to:
\(4y+b = 0 \)
For both equations to have infinite solutions, the 2 equations must be multiples of each other.
However, notice that the first equation has the slope \(-7 \over a\), and the second term has a slope of 0.
Because the 2 slopes are different, there is no ordered pair (a,b) that satisfies the requirements.