+0  
 
0
43
4
avatar+14 

 

For what value of the constant c does the system

have infinitely many solutions?

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

 

PLEASE HELP ASAP angry

 
Web2.0CalcUser123  Oct 13, 2018
 #1
avatar+2389 
+3

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

 
Rom  Oct 13, 2018
 #3
avatar+89996 
+3

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!!!!

 

 

cool cool cool

 
CPhill  Oct 13, 2018
 #4
avatar+14 
+1

Thank you!

 
Web2.0CalcUser123  Oct 13, 2018

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