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

Web2.0CalcUser123
Oct 13, 2018

#1**+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**+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!!!!

CPhill
Oct 13, 2018