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Find B-A if the graph of Ax+By=3 passes through (-7,2) and is parallel to the graph of X+3y=-5

 Mar 24, 2020
 #1
avatar+111330 
+1

 

 

Ax  + By  =  3

 

 

The slope of this line =  -A/B

 

And

 

Since  this line passes through  (-7, 2)  it must be that

 

A(-7) + B(2)  =  3

 

-7A + 2B  =  3

 

2B = 3 + 7A

 

B  =  [ 3 + 7A ] / 2

 

 

And

 

x + 3y  =  - 5

 

3y = -x  - 5      divide  both sides  by  3

 

y = (-1/3)  - 5/3

 

The slope of this line  =  (-1/3)   and since  this line is paralle to the first line e have  that

 

-A/ B  = -1/3

 

A  / B   =  1 / 3

 

A / [ (3 + 7A)/ 2 ] =   1 / 3

 

2A / ( 3 + 7A )  = 1/3     cross-multiply

 

3 * 2A =  1 ( 3 + 7A)

 

6A  = 3  + 7A

 

-A  = 3

 

A = -3

 

B = (3 + 7A) / 2  =  ( 3 + 7(-3)) / 2 =  -18/2  =   -9

 

So

 

A = -3

 

B = -9

 

B - A   =    -9 -  (-3)  =    -6

 

 

cool cool cool

 Mar 24, 2020
 #2
avatar+1970 
+2

Nice, Chris! That's a hard one!!!

CalTheGreat  Mar 24, 2020
 #3
avatar+111330 
0

Thanks, Cal   !!!!

 

 

cool cool cool

CPhill  Mar 24, 2020

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