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For a certain value of k, the system

 

3a + 4b = 7,

6a + 4b = k - 3a - 8b

 

has infinitely many solutions (a,b). What is k?

 Feb 9, 2022
 #1
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Our two equations are:

3a + 4b = 7

9a + 12b = k

 

If (a,b) have infinite many solutions, then those two equations above should be redundant.

If they are redundant, then the second equation is equal to the first equation by a factor of x3.

 

Thus, k = 7 x 3 = 21smiley

 Feb 9, 2022

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