I just answered the second one on your last published question , so I'm solve the first one :
[tex]2x - y \leqslant 5[/tex]
[tex]x + 2y > 2[/tex]
There are two ways to find the answer I just do it in one of them but let me know if u wanna know the other way .
I'm gonna use the options to see which ordered pair is true in both inequalities which is the answer we r looking for :
Option 1 : ( 1 , - 1 )
[tex]2(1) - ( - 1) \leqslant 5[/tex]
[tex]1 + 2( - 1) > 2[/tex]
So ,
[tex]3 \leqslant 5 \: \: \: \: \: true[/tex]
[tex] - 1 > 2 \: \: \: \: \: false[/tex]
So this is not the correct option ..
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Option 2 : ( 4 , 1 )
[tex]2(4) - 1 \leqslant 5[/tex]
[tex]4 + 2(1) > 2[/tex]
So,
[tex]7 \leqslant 5 \: \: \: \: false[/tex]
[tex]6 > 2 \: \: \: \: true[/tex]
Nope ...
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Option 3 : ( 2 , 0 )
[tex]2(2) - 0 \leqslant 5[/tex]
[tex]2 + 2(0) > 2[/tex]
So,
[tex]4 \leqslant 5 \: \: \: \: true[/tex]
[tex]2 > 2 \: \: \: \: \: false[/tex]
Nope....
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The answer must be Option 4 bcuz there's no more options left but let's check it out :
Option 4 : ( 3 , 2 )
[tex]2(3) - 2 \leqslant 5[/tex]
[tex]3 + 2(2) > 2[/tex]
So,
[tex]4 \leqslant 5 \: \: \: \: \: true[/tex]
[tex]7 > 2 \: \: \: \: true[/tex]
There it is ....
