Question

The graph of the following system of equations is:

-2x + y = 3
4x + 2y = 2

Answers-

Overlapping lines

Parallel lines

Intersecting lines

Answer 1

Is it intersecting lines? I plugged them into Desmos but I'm unsure

Answer 2

As all equations are written in the same form
ax+by=c
just find a/b (coefficient of x/coefficient of y) in all cases (or pairs)
wherever a/b is identical the pair of lines are parallel
for eg. in case (a) a/b for line x-2y = 3 is 1/-2 = -2
and for x-2y =1 a/b is again 1/-2 = -2 hence the pair indicated are parallel
in the above cases except for the pair of lines indicated in (d) all the other pairs are parallel
(question (c) is a typo where z should be x)
This is the fastest way of finding out you dont need to rearrange the equation to find slopes. visual finding of a/b is possible
theory is slope of line ax +by +c = 0 is
(-a/b) . hence finding a/b and comparing is enough as all lines are in same form.
lines with equal slopes are parallel