# System of inequalities

#### solakis

##### Active member
Solve the following system of imequalities:
2x+3y-4>0
3x-4y+5>0

MHB Math Helper

#### solakis

##### Active member

Last edited by a moderator:

#### skeeter

##### Well-known member
MHB Math Helper
you posted a challenge problem without knowing the solution beforehand?

for $x > \dfrac{1}{17}$ , $\dfrac{4-2x}{3} < y < \dfrac{3x+5}{4}$

##### Well-known member
I think the question is in wrong section and the original poster is supposed to know the answer before posting.
secondly it is too simple to be in challenging section.

#### anemone

##### MHB POTW Director
Staff member
Hi solakis , thanks for posting at MHB!

I suppose you never realized you have been posted in the "Challenges" subforum. That is okay. No worries.

But I wish to tell you that in this subforum, if you posted a challenge problem here, that usually means you found a problem that is really intriguing and that you have solved it and wanted to share it with the community. In this case, your post is a challenge thread. Or, you found a problem (not a typical math problem) that intrigued you but you couldn't solve it, yet you are interested to know how other people might solve it, you could post that problem here and claimed it as Unsolved Challenge. I hope I have made myself clear.

I welcome you to post again at the appropriate forum if you have any additional or future questions.

#### solakis

##### Active member
my algebraic solution without using graphing is:

(22/17)<y<infinity and (4/3)y-85/51<x<infinity

or

-infinity<y<(22/17) and -(3/2)y +68/34<x<infity

Later i will show in details how i got that solution.

Sorry for the delay but i had a lot of work to do

#### solakis

##### Active member
The solution of the system: 2x+3y-4=0, 3x-4y+5=0 are:
x=1/17 and y=22/17.

#### solakis

##### Active member
my algebraic solution without using graphing is:

(22/17)<y<infinity and (4/3)y-85/51<x<infinity

or

-infinity<y<(22/17) and -(3/2)y +68/34<x<infity

Later i will show in details how i got that solution.

Sorry for the delay but i had a lot of work to do
The solution of the system: 2x+3y-4=0, 3x-4y+5=0 are:
x=1/17 and y=22/17.

Now put:
x=1/17+n and y =22/17 +m ................................................................(1)
and substituting those back to the original inequalities we get:

2m+3n>0 and 3m-4n>0
or
m>-(2/3)n and m>(4/3)n...............................................(2)
Now we have the following cases:
a)n is a positive No.Then from (2) we have:

m>(4/3)n and from this inequality and (1) we have:

22/17<y<infinity and (4/3)y-(85/51)<x<infinity......................................(3)

b)for n negative ,then from (2) we have :

m>-(3/2)n,and from this inequality and (1) we have:

-infinity<y<22/17 and-(3/2)y+68/34<x<infinity.............................................(4)

Hence the solution of the inequalities are (3 ) ,(4)