Question 418609
Instead of the extremely verbose yet tedious solution the other tutor posted using the pluggable solvers, we can determine which system has no solutions without solving each system or graphing.


First note that any two lines of different slope must intersect at exactly one point. Also, if two lines have the same slope, they are either parallel (no solution) or are the same line (infinitely many solutions). We start by finding the slopes of each line.


5x+2y = 4
2x-2y = 10


Rewriting each in y = mx + b form, we obtain:


y = (-5/2)x + 2
y = 2x - 10 Hence, this system has a solution.


Repeat the same for the other three systems:


y = (-1/3)x - 1/3
y = (1/3)x + 1/3, solution exists


y = (1/2)x + 3
y = (1/2)x + 3 These two lines are the same, so infinitely many solutions.


y = (1/2)x + 1/2
y = (1/2)x These lines are parallel and do not intersect. So, choice 4 has no solution.