Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
The point [tex](-2,2)[/tex] is a solution of the system given by [tex]y<2x+8[/tex] and [tex]y \geq -x-3[/tex]
Given point: [tex](-2,2)[/tex]
Given systems:
- [tex]y>-2x+2[/tex] and [tex]y>x+5[/tex]
- [tex]y<x+2[/tex] and [tex]y>x-1[/tex]
- [tex]y<2x+8[/tex] and [tex]y \geq -x-3[/tex]
- [tex]y<2x+3[/tex] and [tex]y \geq -2x-5[/tex]
To find: The system to which the given point is a solution
If a point is a solution of a system, then the coordinates of the point satisfies all the equation(s) or inequation(s) of the system. So, we can substitute the x & y coordinates of the given point into the inequalities of each of the given systems and check if the inequalities are satisfied by the coordinates of the point.
(1) [tex]y>-2x+2[/tex] and [tex]y>x+5[/tex]
Substitute the coordinates of the point [tex](-2,2)[/tex] into the inequalities of the system.
Put [tex]x=-2,y=2[/tex] in [tex]y>-2x+2[/tex] to get,
[tex]2>-2(-2)+2[/tex]
[tex]2>4+2[/tex]
[tex]2>6[/tex]
The above inequality is clearly impossible and thus, the coordinates of the given point does not satisfy this inequality.
This implies that the given point is not a solution of this system.
(2) [tex]y<x+2[/tex] and [tex]y>x-1[/tex]
Substitute the coordinates of the point [tex](-2,2)[/tex] into the inequalities of the system.
Put [tex]x=-2,y=2[/tex] in [tex]y<x+2[/tex] to get,
[tex]2<-2+2[/tex]
[tex]2<0[/tex]
The above inequality is clearly impossible and thus, the coordinates of the given point does not satisfy this inequality.
This implies that the given point is not a solution of this system.
(3) [tex]y<2x+8[/tex] and [tex]y \geq -x-3[/tex]
Substitute the coordinates of the point [tex](-2,2)[/tex] into the inequalities of the system.
Put [tex]x=-2,y=2[/tex] in [tex]y<2x+8[/tex] to get,
[tex]2<2(-2)+8[/tex]
[tex]2<-4+8[/tex]
[tex]2<4[/tex]
This is a true inequality. Then, the given point satisfies the first inequality of the system.
We will now check if the point satisfies the second inequality of the system.
Put [tex]x=-2,y=2[/tex] in [tex]y \geq -x-3[/tex] to get,
[tex]2 \geq -(-2)-3[/tex]
[tex]2 \geq 2-3[/tex]
[tex]2 \geq -1[/tex]
This is also a true inequality. Then, the given point also satisfies the second inequality of the system.
Thus, the given point is a solution of this system.
(4) [tex]y<2x+3[/tex] and [tex]y \geq -2x-5[/tex]
Substitute the coordinates of the point [tex](-2,2)[/tex] into the inequalities of the system.
Put [tex]x=-2,y=2[/tex] in [tex]y<2x+3[/tex] to get,
[tex]2<2(-2)+3[/tex]
[tex]2<-4+3[/tex]
[tex]2<-1[/tex]
The above inequality is clearly impossible and thus, the coordinates of the given point does not satisfy this inequality.
This implies that the given point is not a solution of this system.
Thus, we can see that the coordinates of the given point [tex](-2,2)[/tex] satisfies the inequalities of the third system only.
Then, the point [tex](-2,2)[/tex] is a solution of the system given by [tex]y<2x+8[/tex] and [tex]y \geq -x-3[/tex].
Learn more about geometric solutions of system of linear inequalities here:
https://brainly.com/question/17174433
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
