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

 Aug 11, 2022
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A = -3 and B = -9

 

Since Ax + By = 3 is parallel to 1x + 3y = -5, we know that A/B = 1/3 or 3A = B

 

Next we are given that Ax + By = 3 intersects (-7, 2) so -7A + 2B = 3

 

Now using substitution we can solve for A and B

 

-7A + 2(3A) = 3

-7A + 6A = 3

-A = 3

A = -3

 

B = 3A

B = 3(-3)

B = -9

 Aug 11, 2022

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