1) Let's rewrite each inequality by making some algebraic manipulations:
4x -3y < -3
-x +3y > -6
2) Turning from the Standard form to slope-intercept
4x -3y < -3 Subtract 4x from both sides
-3y < -3 -4x Divide both sides by -3
y > 4/3x +1 Multiplying or Dividing by negative numbers swaps the sign too.
-x +3y > -6 Add x from both sides
3y > -6 -x Divide both sides by 3
y >-2 +x/3
3) Plotting the graph
The possible solutions are in the darker common shaded area, so
(-3,1)
