True or false, there is no solution to the systems of inequalities shown below

y<3x+5

y>-x+4

False.

there are solutions to this system of inequalities.

-> For a quick check you can take random x, e. g. consider x=0, and substitute it in the inequality, which gives

y4.

there are infinite number of y satisfying these conditions.

-> You can solve it graphically to get exact solution. draw the line y=3x+5 and y = - x+4. The common region, below y=3x+5 and above y=-x+4, is the solution for the system of inequalities.