Fas which graph shows the solution to the system of linear inequalities ? x - 4y is less than or equal to 4 y < x + 1

Well, we do not see the lines clearly (if they are dotted (inequality) or solid (inequality or equal) ), but we'll come back to this.

y<x+1  can be simplified to be y<x if we ignore the constants, so the valid part is BELOW the line, since (y<)

x-4y <=4
again, ignore the constants and simplify to 
x-y<0 or
y>x   so the valid part is ABOVE the line (since y>)

There are two graphs that satisfy BOTH conditions, pink (slope=1) at the bottom, and blue (slope = 1/4) on top, i.e. first and third graph.

For the absolute inequality (y<x+1), the red line must be dotted.
For the <= condition, the blue line must be solid.

As we cannot see the lines clearly, you will make the choice between the first and third graphs according to the previous paragraph.