Trouble reading intersection points when solving simultaneous equations by graph

I’m revising simultaneous equations by graph to strengthen my fundamentals, but I keep second-guessing how I’m plotting and reading the intersection.

Example 1: 2x + y = 5 and y = x − 1. I rewrote the first as y = −2x + 5. For y = −2x + 5, I used intercepts: x-intercept at 2.5 (when y = 0) and y-intercept at 5 (when x = 0). For y = x − 1, I plotted (0, −1) and used slope 1 to go up 1, right 1. With a 1-unit grid, my lines look like they cross slightly off a grid point, and I keep reading something like x ≈ 1.9, y ≈ 0.9. I’m worried I’m introducing error. Are my chosen points sensible here, or is there a better way to pick points to make the intersection land more cleanly on the paper?

Example 2: y = 0.5x − 2 and y = −2x + 1. I plotted (0, −2) and (4, 0) for the first line, and (0, 1) and (1, −1) for the second. On my graph paper, the intersection looks around (1.3, −1.3), but I’m not confident about reading tenths from a hand-drawn graph. How do you choose a good scale so fractional intersections are readable? Is there a reliable way to estimate to the nearest tenth without it being a guess?

Also, is there a quick check from the equations themselves to know ahead of time if the lines will be parallel or actually the same line, so I don’t find out only after drawing?

If anyone can walk me through a careful, step-by-step way to pick points, set a scale, and read off the solution accurately (including what to double-check if the intersection doesn’t land on a neat grid point), that would really help me tighten up my graphing.