Question

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

y<3x+5
y>-x+4

Answer 1

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
y<5 and y>4 .
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.

Answer 2

False
Because if you plot a graph to both the equation as i have attached the image.. you can see there can be multiple solution to the above system of inequalities.