My mind is blown

3x + 4y = 7

6x + 4y  = c - 4y  →  6x + 8y  =  c

The second equation will be a multiple of the first when c  =  14

And this value of c will result  in infinite solutions  for the system

My mind is blown

For what value of the constant $c$ does the system $$\begin{align*} 3x + 4y &= 7,\\ 6x + 4y &= c- 4y, \end{align*}$$ have infinitely many solutions?

Hello guest!

$3x + 4y = 7,\\ 6x + 4y = c- 4y$

$3x+4y=\frac{c}{2}\\ \frac{c}{2}=7\\ \color{blue} c=14$

At c = 14 this system of equations has infinitely many results.

  !