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For every value of a, the graph of each of these three equations is a line:

ax + y = 1

x  + ay = 1

x + y = 9

 

For what value of a do all three of these lines intersect at the same point?

 Mar 1, 2022
 #1
avatar+122390 
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Add the first two equations

 

ax + y  + x + ay   = 2      simplify

 

a ( x + y)  + (x + y)  =    2                                        { remember that  x + y  =  9 }

 

a (9)  + (9)  =  2

 

9a  =  2  - 9

 

9a  =  -7

 

a   = -7/9

 

See the graph here   :    https://www.desmos.com/calculator/1tn3bcfeqk

 

cool cool cool

 Mar 1, 2022

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