Sketch the graph of the solution set of each system of inequalities.
2x-5y<-6 and 3x+y<8

1) 2x-5y<-6
rearrange to

5y \,\gt\, 2x+6

y \,\gt\, \frac 25x + \frac 65

2) 3x+y<8

rearrange to

y \lt -3x+8

1. draw the two lines indicated by the equations. Slope/Intercept is appropriate since the equations are in that form.

2. Note that the "<" or ">" implies that the inequalities do not include the lines. Figure out which side of the line is included in the inequality (pick a point, plug it into the equation and see if it fits).

3) The intersection of the two areas is the graph required.