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HALPPPP! For a certain value of $k,$ the system \begin{align*} 3a + 4b &= 7,\\ 6a + 4b &= k- 4b \end{align*}has infinitely many solutions $(a,b).$ What is $k$? I had this question on my math test. Got my results, but they didn't tell me correct answer. Plz tell me correct answer with steps so i know how i got it wrong.

Jul 22, 2021

#1
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3a  +  4b   =  7       multiply  through  by 2

6a   +  8b   =  14

And note  that  the second equation simplifies to

6a  + 8b  =  k

Which....if we have infinite solutions implies  that  k =   14

Jul 22, 2021
#2
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Thank you. I understand now.

Jul 22, 2021