Solving for Point D: How to Find the Intersection of Two Linear Equations

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In summary, the problem involves finding the intersection of two lines x + y = 275 and 225x + 250y = 63000. The solution is (230, 45) and involves solving a system of two equations in two unknowns.
  • #1
hyde2042
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Homework Statement



The problem:

[2] http://i.imgur.com/C5VwZ.png

Homework Equations


So I got the constraints to be

1.x+y(less than or equal to) 275

2.225x+250y (less than or equal to) 63,000

3. x and y (Greater than) 0

So if the line from point A is extrapolated, then where it hits the x-axis would be constraint 2 and point C is constraint 1.

The Attempt at a Solution



The graph I ended up with:

[1] http://i.imgur.com/9jJYt.png
 
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  • #2
hyde2042 said:

Homework Statement



The problem:

[2] http://i.imgur.com/C5VwZ.png

Homework Equations


So I got the constraints to be

1.x+y(less than or equal to) 275

2.225x+250y (less than or equal to) 63,000

3. x and y (Greater than) 0

So if the line from point A is extrapolated, then where it hits the x-axis would be constraint 2 and point C is constraint 1.

The Attempt at a Solution



The graph I ended up with:

[1] http://i.imgur.com/9jJYt.png

Point D is where the line x + y = 275 intersects with the line 225x + 250y = 63000. This is a simple matter of solving a system of two equations in two unknowns.

The problem you posted in your first link seems to have nothing to do with what you're doing here.
 
  • #3
Whoops. Sorry about the wrong post.

When I set the two equal to each other. -x + 275 = (225/250)x + (63000/250) I'm getting the incorrect answer.

The book says it should be (230, 45)

I keep getting (12.1, 262.9)
 
  • #4
hyde2042 said:
Whoops. Sorry about the wrong post.

When I set the two equal to each other. -x + 275 = (225/250)x + (63000/250) I'm getting the incorrect answer.
You have a sign wrong in the right side. Solving the second equation for y gives y = -(225/250)x + 63000.

I get the right answer.
hyde2042 said:
The book says it should be (230, 45)

I keep getting (12.1, 262.9)
 

1. How do I determine the coordinates of point D on a graph?

In order to find point D on a graph, you will need to know the coordinates of at least two other points. Use the slope formula or the distance formula to calculate the missing coordinate.

2. What is the difference between finding a point on a line and finding a point on a curve?

When finding a point on a line, you can use the slope formula or the equation of the line to determine the coordinates. However, when finding a point on a curve, you may need to use calculus and derivatives to find the slope at a specific point, which can then be used to find the coordinates.

3. Can I use any two points to find point D on a graph?

No, in order to accurately find point D, the two points you use must be on the same line or curve. Otherwise, the calculated coordinates of point D may not be correct.

4. Is there a specific method for finding point D on a three-dimensional graph?

Yes, finding point D on a three-dimensional graph requires using the distance formula in three dimensions. You will need to know the coordinates of at least three points in order to accurately find the coordinates of point D.

5. Can I use a graphing calculator to find point D?

Yes, most graphing calculators have functions that allow you to input the coordinates of two points and calculate the coordinates of a third point. However, it is still important to understand the mathematical concepts behind finding a point on a graph in order to accurately interpret the results given by the calculator.

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