SOLUTION: Hi all, was just wondering if someone could show me what the correct way to complete and show all working for the following problems. There are a few seperate problems I have to do

Algebra ->  Equations -> SOLUTION: Hi all, was just wondering if someone could show me what the correct way to complete and show all working for the following problems. There are a few seperate problems I have to do      Log On


   

Question 200359: Hi all, was just wondering if someone could show me what the correct way to complete and show all working for the following problems. There are a few seperate problems I have to do. I need to solve for x and y for the following.
1. 5x -2y = 1
2. 2x+ y = 11
3. 5x - 3y = 1
Thnaks guys, -Nick.
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Hi all, was just wondering if someone could show me what the correct way to complete and show all working for the following problems. There are a few seperate problems I have to do. I need to solve for x and y for the following.
1. 5x -2y = 1
2. 2x+ y = 11
3. 5x - 3y = 1
-----------------
Those 3 don't have a solution that works for all of them. 2 variables require 2 equations, not 3.
You can take any 2 of the 3 and find a solution.
If you graph these three, they don't have a common intersection point, they make a triangle.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Alan didn't know what you were supposed to do. Here's Edwin's solution:

1. 5x-2y+=+1

Solve for x:

5x-2y+=+1

Add %22%22%2B2y to both sides:

5x-2y%2B2y+=+1%2B2y

5x-cross%282y%29%2Bcross%282y%29+=+1%2B2y

5x+=+1%2B2y

Divide both sides by 5.  This can be
done either of two ways:

1. Divide the whole right side by 5

%285x%29%2F5+=+%281%2B2y%29%2F5


%28cross%285%29x%29%2Fcross%285%29+=+%281%2B2y%29%2F5

x+=+%281%2B2y%29%2F5

2. Divide each term individually by 5:

%285x%29%2F5+=+1%2F5%2B%282y%29%2F5

%28cross%285%29x%29%2Fcross%285%29=+1%2F5%2B%282y%29%2F5

x=1%2F5%2B%282y%29%2F5

Both answers are correct and equivalent.

---

Solve for y:

5x-2y+=+1

Add -5x to both sides:

5x-5x-2y+=+1-5x

cross%285x%29-cross%285x%29-2y+=+1-5x

-2y+=+1-5x

Divide both sides by -2.  This can be
done either of two ways:

1. Divide the whole right side by -2

%28-2y%29%2F-2+=+%281-5x%29%2F-2

%28cross%28-2%29y%29%2Fcross%28-2%29+=+%281-5x%29%2F-2

y+=+%281-5x%29%2F-2

2. Divide each term individually by 5:

%28-2y%29%2F-2+=+1%2F-2-%285x%29%2F-2

or canceling on the left simplifying the signs
on the right:

%28cross%28-2%29y%29%2Fcross%28-2%29=+-1%2F2%2B%285x%29%2F2

y=-1%2F2%2B%282y%29%2F5

Both answers are correct and equivalent.

2. 2x%2By+=+11

Same way:

x=%2811-y%29%2F2 or x=11%2F2-y%2F2

y=11-2x 


3. 5x - 3y = 1

Same way:

x=%281%2B3y%29%2F5 or x=1%2F5%2B%283y%29%2F5

y=%281-5x%29%2F%28-3%29 or y=-1%2F3%2B%285x%29%2F3

Edwin