The lines A, 2x + 3y = 19 and B, 2x + 3y + 7 = 0 also a line C, 2x + 3y = 6.

Let d₁ be the distance between lines 2x + 3y = 19 and 2x + 3y = 6,

While d₂ is the distance between lines 2x + 3y + 7 = 0 and 2x + 3y = 6

Hence proved, the lines 2x + 3y = 19 and 2x + 3y + 7 = 0 are equidistant from the line 2x + 3y = 6