Intersection of inequalities problem.

If it does, then it is a point of intersection.In summary, to find the numbers for S∩T where S is x^2+y^2 <=100 and T is x+y<=14, you can graph the equations and identify points of intersection by looking at the different plane regions formed by the graphs. Then, choose a point in each region and test if it satisfies both equations to determine the points of intersection. Alternatively, you can add the equations and solve for x and y, but this method may not always work. A Venn diagram can also be used to visualize the intersection.
  • #1
Demonoid
14
0
I need to graph/find numbers for S∩T where S is x^2+y^2 <=100 and T is x+y<=14.

I know I can find them simply by choosing/picking them, but are there any other solution ?

I thought maybe doing

x^2+y^2 <=100
+
x+y<=14
=
x^2+y^2 + x+y<=14 +100 =
x^2+y^2 + x+y<=114 =
x^2+y^2 <= 114-x-y =
x+y <= sqrt(114-x-y) <-- doesn't work for x=7 and y=7 ?

OR am I doing something wrong ?

Venn diagram confirms that to find an intersection I need to add them and this should yield the result, but this doesn't work ? why ??

thank you for any responses !:D
 
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  • #2
Graph the equations and identify points of intersection. Look for the different plane regions which the graphs form. Pick a point in each region and test if the point satisfies both equations.
 

FAQ: Intersection of inequalities problem.

What is the intersection of inequalities problem?

The intersection of inequalities problem involves finding the simultaneous solutions to multiple inequalities. It is often represented on a graph as the overlapping region between two or more inequality lines.

How do you solve an intersection of inequalities problem?

To solve an intersection of inequalities problem, you can use a graphing calculator or manually graph the inequalities on a graph. The solution is then found by identifying the overlapping region.

What is the significance of the intersection of inequalities problem?

The intersection of inequalities problem is important in mathematics and science because it allows us to find the common solutions to multiple inequalities. This is useful in various fields such as economics, engineering, and statistics.

What are some common strategies for solving the intersection of inequalities problem?

Some common strategies for solving the intersection of inequalities problem include graphing the inequalities, using substitution or elimination methods, and using the properties of inequalities to simplify the problem.

Can the intersection of inequalities problem have no solution?

Yes, it is possible for the intersection of inequalities problem to have no solution. This occurs when the inequalities do not overlap or when the overlapping region is a single point or line. In these cases, there is no common solution to the inequalities.

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