See if the distance between the two lines is consistent with a compass.
Make sure the lines intersect at right angles with the corner of a piece of paper.
Measure each of the angles with a straightedge.
There is no way to ensure you have constructed parallel lines.
To have infinitely many solutions they must describe the same line. So any multiple or fraction of the reference line would indeed describe the same line, and thus "intersect" at each and every of an infinite number of points.
2(x+y=4)
2x+2y=8 (is the same line as x+y=4)
43.71, 43.6, 41.92 greatest to least