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# NEED HELP NOW

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For what value of the constant c does the system

have infinitely many solutions?

\begin{align*} 3x + 4y &= 7,\\ 6x + 4y &= c- 4y, \end{align*}

Oct 13, 2018

#1
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$$\text{we need the lines to have the same slope and intercept}\\ 3x+4y=7 \Rightarrow y = -\dfrac 3 4 x + \dfrac 7 4\\ 6x+4y=c-4y \Rightarrow y= -\dfrac 3 4 x + \dfrac c 8\\ \dfrac c 8 = \dfrac 7 4 \\ c = 14$$

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Oct 13, 2018
#3
+99736
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The system will have infinite solutions when both equations are  exactly the same

Note that we can add 4y to both sides of the second equation and get

6x + 8y   =  c

Notice that the left side is just a multiple  [ of 2 ] of the left side of the  first equation

So...multiplying the right side of the first equation by 2  gives us 14  = c  and both equations will be exactly the same.....so....the system will have infinite solutions!!!!

Oct 13, 2018
#4
+78
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Thank you!

Oct 13, 2018