LVG solution at a kinetic temperature ﹩T_{K}=30﹩ K for the CO line ratios for M17 averaged over the entire cloud. The lines indicate the observed ±1 σ values for the line ratios ¹²CO/¹³CO ﹩J=2\rightarrow 1﹩ (﹩4.5\pm 0.7﹩; solid line); ¹²CO/¹³CO ﹩J=3\rightarrow 2﹩ (﹩3.7\pm 0.9﹩; dashed line); ¹²CO (﹩J=3\rightarrow 2﹩)/(﹩J=2\rightarrow 1﹩) (﹩0.76\pm 0.19﹩; dot‐dashed line; lower limit in lower left corner, upper limit along lower right); and ¹³CO (﹩J=3\rightarrow 2﹩)/(﹩J=2\rightarrow 1﹩) (﹩1.3\pm 0.3﹩; dotted line; only the lower limit appears in the figure). The hatched area indicates the region where all four sets of lines intersect, and the black area encompasses the region where ﹩\Delta \chi ^{2}\leq 1﹩.