First we need a line that passes through (3,2) that looks like ax+5y=b, where a is the number in the first box and b is the number in the second box. We plug in x=3 and y=2: 3a+10=b, so we have b in terms of a.
We need to find a value of a (which gives us a related value for b) so that when we combine the equation with the given one there are no solutions to the system of equations.
Graphically, the solution to a system of two linear equations is found by plotting the lines and looking at the point where they intersect. If the lines are parallel they won’t intersect and there will be no solution. So I think that’s what this question is all about. Two lines are parallel when the coefficients of the x and y terms match. So if we put a=10, then b=40 and the answer would be 10x+5y=40. There are no solutions to the system: 10x+5y=15 and 10x+5y=40. These lines when plotted are parallel. The identical quantities on the left can’t add up to two different values (15 and 40) so the system is inconsistent and there are no solutions.