SOLUTION: The graphs of the equations 2x - By = 7 and Ax + 3y = 10 are both the same line. Find A and B.

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Question 1174560: The graphs of the equations 2x - By = 7 and Ax + 3y = 10 are both the same line.
Find A and B.
Found 2 solutions by ewatrrr, greenestamps:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
  y = 2x/B - 7/B
  y = -Ax/3 + 10/3
Same Lines: 
      2x/B = -Ax/3  ⇒ AB = -6   
  and -7/B = 10/3  ⇒ B = -21/10    
                   AB =- -6 ⇒  A(-21/10) = -6  and  A = 20/7 

Wish You the Best in your Studies.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If the equations are to be of the same line, then the two equations in Px+Qy=C should both have the same constant C.

So multiply the first equation by 10/7. Then we have

%2820%2F7%29x-%2810B%2F7%29y+=+10
Ax%2B3y+=+10

Now, since these equations are the same,

A+=+20%2F7

and

-10B%2F7+=+3
-10B+=+21
B+=+-21%2F10

ANSWERS: A = 20/7; B = -21/10