There are no solutions to the system of inequalities shown below. y < -2x + 7 y > 3x + 1

Question

There are no solutions to the system of inequalities shown below.

y	<	-2x + 7
y	>	3x + 1

 

Answer 1

No, there is a solution to it

y<-2x+7

y>3x+1

 

For x < 6/5  it would be 1 + 3 x < y < 7 - 2 x. 

For each x from (-∞, 6/5) you can find an interval for y, where both inequalities hold. For example if x=0, then 1<y<7, if x=-5, then -14<y<17.

But if x>6/5, then there is no  such y: 1 + 3 x < y < 7 - 2 x. 

For example, if x=2, the inequality 1+3x<y<7-2x doesn't hold.