# Solve System of Inequalities: 2x+3y-4, 3x-4y+5

• MHB
• solakis1
In summary: SoIn summary, the solution of the system of inequalities 2x+3y-4>0 and 3x-4y+5>0 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.
solakis1
Solve the following system of imequalities:
2x+3y-4>0
3x-4y+5>0

skeeter said:
https://www.physicsforums.com/attachments/10382

Last edited by a moderator:
solakis said:

you posted a challenge problem without knowing the solution beforehand?

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

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.

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.(Smile)

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

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.

solakis said:
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

[sp]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)[/sp]

## 1. How do you graph a system of inequalities?

To graph a system of inequalities, you first need to plot the boundary lines for each inequality. Then, shade the region that satisfies all of the inequalities. The solution to the system of inequalities is the shaded region.

## 2. How do you write a system of inequalities in standard form?

To write a system of inequalities in standard form, you need to rearrange the equations so that the variables are on the left side and the constants are on the right side. The inequalities should also be written with the variable on the left side and the constant on the right side.

## 3. What is the difference between a system of inequalities and a system of equations?

A system of inequalities involves inequalities (>, <, ≥, ≤) while a system of equations involves equations (=). In a system of inequalities, the solution is a range of values that satisfy all of the inequalities, while in a system of equations, the solution is a specific point that satisfies all of the equations.

## 4. How do you solve a system of inequalities algebraically?

To solve a system of inequalities algebraically, you need to isolate one variable in one of the inequalities and substitute it into the other inequality. This will result in a single inequality with one variable, which can then be solved to find the range of values for that variable. Repeat this process for the other variable to find the complete solution.

## 5. Can a system of inequalities have no solution?

Yes, a system of inequalities can have no solution if the inequalities are contradictory or if the solution is outside of the given range of values. For example, if one inequality is x > 5 and the other is x < 3, there is no value of x that satisfies both inequalities.

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