\(Given\)To find Intersections, straight line equations are set to each other, but parallel lines don't intersect, and this is proven when the variables cancel out.
Note: This can also be shown by noting they have same slope, which is the value multiplied to x (or whatever other variable name).
\(2x + 3\)
\(and\)
\(2x + 5\)
\(2x + 3 = 2x + 5\)
\(2x - 2x + 3 = 2x - 2x + 5\)
\(Variables\,\,are\,\, canceling\,\,out\,\,\)\(therefore\,\,showing\,\,no\,\, intersection.\)
