# Inequality from GRE

So I was helping my gf go over some GRE math questions, and we came across a strange question.

Solve for x and y
x=2y
5x<y+7

I said that the answer would be

y<7/9 and x<14/9

this is the right answer, but she asked how that works. How do both the equality and inequality hold true at the same time? Shouldn't the answer be undetermined? I don't quite know how to answer the question. My opinion is that as long as both x and y are less than their respective inequality, then the equality will then hold.

Are there any more precise thoughts or theories regarding the subject?

Pengwuino
Gold Member
If that is the right answer, it simply means that x and y have to simultaneously satisfy the conditions that y<7/ and x<14/9 and x=2y. So in other words, x = -5 and y = -3 would not satisfy the equation but x = -5 and y = -2.5 will. Your idea is a bit backwards, the equality holding is a much stronger condition but in the end, one condition being being true doesn't mean other is true

Last edited:
vela
Staff Emeritus
Homework Helper
The inequality 5x<y+7 corresponds to the half plane above the line y=5x-7. The solutions correspond to the portion of the line x=2y that lies in that half plane.

HallsofIvy