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For every value of $a$, the graph of each of these three equations is a line: \begin{align*} ax+y &= 1, \\ x + ay &= 1, \\ x + y &= 6. \end{align*}For what value of $a$ do all three of these lines intersect at the same point?

 Apr 9, 2021
 #1
avatar+121004 
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Add  the  first two equations  and we  get  that

 

(a + 1) x   +  (a + 1)  = 2

 

(a + 1) ( x + y)  =  2

 

(a + 1) (6)  =  2

 

(a + 1)  =  2/6

 

a + 1  =  1/3

 

a =  1/3  - 1   =   -2/3

 

See the  graph here  :   https://www.desmos.com/calculator/oy66se779q

 

 

 

cool cool cool

 Apr 9, 2021

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