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#1 2022-06-09 20:26:49
- jadewest
- Member
- Registered: 2021-02-20
- Posts: 44
Linear Inequalities
Hello,
I am having trouble solving this system of inequalities and graphing it:
2x > -4y
4y - 2x < 8
Thank you,
Jade
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#2 2022-06-09 21:57:42
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,402
Re: Linear Inequalities
Hi jadewest,
Given:
Equation : 2x - 4y = 8
To Find:
Three different solutions.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#3 2022-06-10 01:10:39
- jadewest
- Member
- Registered: 2021-02-20
- Posts: 44
Re: Linear Inequalities
Hello,
I'm having trouble finding the solution for this:
2x > -4y
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#4 2022-06-10 01:53:19
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,402
Re: Linear Inequalities
Hi,
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#5 2022-06-11 21:27:29
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,621
Re: Linear Inequalities
hi jadewest
Here's how to make the graph.
Start by drawing the lines 2x = -4y and 4y - 2x =8
On each line the left side of the equation equals the right side.
On one side of a line the inequality < will work and on the other side the inequality > will apply. So you need to decode which side of the line is correct in each case.
I choose a random point that is not on either line. To keepthe arithmetic simple I chose (1,1)
Substitute x = 1 y = 1 into 2x and -4y. I could see that (2 times 1) is greater than (minus 4 times 1) so (1,1) is in the required region. If you try, say, x = -3, y = -2 you will find (2 times -3) < (-4 times -2) so this point is NOT in the required region. So we've got to be above that line (2x = -4y).
Substitute x = 1 y = 1 into 4y - 2x = 4 - 2 < 8. So once again (1,1) is in the required region, ie. below the line 4y - 2x = 8.
The two lines divide the graph into 4 spaces. I have shaded yellow the area which satisfies both inequalities.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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