Answer: infinite solutions
Step-by-step explanation:
These equations are both equations of lines - 'linear equations'. The solutions, if any, will be where the lines intersect. If they are actually the same line, they will have infinite points in common, and thus an infinite number of solutions. If they are parallel, they never intersect, so there is no soltion at all. If they are 2 distinctly different lines and not parallel, geometry tells us they will intersect at exactly one point. There is no way for two lines to intersect at exactly 2 points, so that answer is no good from the start. Only choices are 0, 1, infinite.
Let's see . . . .
We have -5x + y = -18
and 10x - 2y = 36
When I line them up like this, I notice that all the coefficients in the second equation are twice the magnitude of the corresponding ones in the first equation. I also notice that in the second equation, each coeffient is the opposite, or negative, of the corresponding coefficient in the first equation. When I put these two observations together, I see that the second eqaution is really just the 1st equation multiplied by (-2)! Multiplying both sides of an equation by the same nonzero number doesn't really change anything, so we don't actually have the equations of 2 different lines. (Try graphing them if you want to demonstrate this to yourself.) They are really the same line, just expressed 2 different ways.
They intersect at every point, so the solutions are infinite.