1. Examples
1. Draw lines : x+y=4;x+2y=6
Solution:
1. To draw constraint `color{red}{x+y=4} ->(1)`
When `x=0` then `y=?`
`=>(0)+y=4`
`=>y=4`
When `y=0` then `x=?`
`=>x+(0)=4`
`=>x=4`
2. To draw constraint `color{green}{x+2y=6} ->(2)`
When `x=0` then `y=?`
`=>(0)+2y=6`
`=>2y=6`
`=>y=(6)/(2)=3`
When `y=0` then `x=?`
`=>x+2(0)=6`
`=>x=6`
2. Draw lines : x+y<=4;x+2y>=6
Solution:
1. To draw constraint `color{red}{x+y<=4} ->(1)`
Treat it as `color{red}{x+y=4}`
When `x=0` then `y=?`
`=>(0)+y=4`
`=>y=4`
When `y=0` then `x=?`
`=>x+(0)=4`
`=>x=4`
Put `x=0,y=0` (origin) in `color{red}{x+y<=4}`, then `0+0<=4`, which is true,
The half plane containing the origin is the region of the solution set of the inequation `color{red}{x+y<=4}`
2. To draw constraint `color{green}{x+2y>=6} ->(2)`
Treat it as `color{green}{x+2y=6}`
When `x=0` then `y=?`
`=>(0)+2y=6`
`=>2y=6`
`=>y=(6)/(2)=3`
When `y=0` then `x=?`
`=>x+2(0)=6`
`=>x=6`
Put `x=0,y=0` (origin) in `color{green}{x+2y>=6}`, then `0+0>=6`, which is false,
The half plane not containing the origin is the region of the solution set of the inequation `color{green}{x+2y>=6}`
3. Draw lines : x+y>=4;x+2y<=6
Solution:
1. To draw constraint `color{red}{x+y>=4} ->(1)`
Treat it as `color{red}{x+y=4}`
When `x=0` then `y=?`
`=>(0)+y=4`
`=>y=4`
When `y=0` then `x=?`
`=>x+(0)=4`
`=>x=4`
Put `x=0,y=0` (origin) in `color{red}{x+y>=4}`, then `0+0>=4`, which is false,
The half plane not containing the origin is the region of the solution set of the inequation `color{red}{x+y>=4}`
2. To draw constraint `color{green}{x+2y<=6} ->(2)`
Treat it as `color{green}{x+2y=6}`
When `x=0` then `y=?`
`=>(0)+2y=6`
`=>2y=6`
`=>y=(6)/(2)=3`
When `y=0` then `x=?`
`=>x+2(0)=6`
`=>x=6`
Put `x=0,y=0` (origin) in `color{green}{x+2y<=6}`, then `0+0<=6`, which is true,
The half plane containing the origin is the region of the solution set of the inequation `color{green}{x+2y<=6}`
4. Draw lines : 3x-y>=6;-5x+y<=5
Solution:
1. To draw constraint `color{red}{3x-y>=6} ->(1)`
Treat it as `color{red}{3x-y=6}`
When `x=0` then `y=?`
`=>3(0)-y=6`
`=>-y=6`
`=>y=-6`
When `y=0` then `x=?`
`=>3x-(0)=6`
`=>3x=6`
`=>x=(6)/(3)=2`
Put `x=0,y=0` (origin) in `color{red}{3x-y>=6}`, then `0+0>=6`, which is false,
The half plane not containing the origin is the region of the solution set of the inequation `color{red}{3x-y>=6}`
2. To draw constraint `color{green}{-5x+y<=5} ->(2)`
Treat it as `color{green}{-5x+y=5}`
When `x=0` then `y=?`
`=>-5(0)+y=5`
`=>y=5`
When `y=0` then `x=?`
`=>-5x+(0)=5`
`=>-5x=5`
`=>x=(5)/(-5)=-1`
Put `x=0,y=0` (origin) in `color{green}{-5x+y<=5}`, then `0+0<=5`, which is true,
The half plane containing the origin is the region of the solution set of the inequation `color{green}{-5x+y<=5}`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
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