Question

When is it possible for a system of two inequalities to have no solution?

Answer 1

when it leads to a contradiction\[x+y=1\]\[x+y=2\]subtract the first from the second and you get\[0=1\]which is never true

Answer 2

Those are not inequalities guys.

Answer 3

\[x+y<1\]\[x+y>1\]

Answer 4

But the idea is right. If the system leads you to a contradiction.

Answer 5

thank you guys <3

Answer 6

thanks no-data, your english is better than mine today I guess :P

Answer 7

Thanks TT =)

Answer 8

Inequalities are solution regions. You could have two regions that do not intersect at all.

Answer 9

@precal You mean: The solution of an inequality is a region. So if you have two inequalities you have two regions. If these regions do not intersect then there is no solution for the system.In other words the solution is the empty set.

Answer 10

Yes, nicely put.