Answer:
The value of \(b\) will be -8.
Step-by-step explanation:
The two given equations are.....
\(3y+12=6x...........................(1)\\ \\ 2y=4x+b.............................(2)\)
From equation (1), we will get......
\(3y=6x-12\\ \\ \frac{3y}{3}=\frac{6x-12}{3}\\ \\ y=2x-4\)
From equation (2), we will get.....
\(2y=4x+b\\ \\ \frac{2y}{2}=\frac{4x+b}{2}\\ \\ y=2x+\frac{b}{2}\)
For getting the solution of the system as "infinitely many solutions" , both equations \(y=2x-4\) and \(y=2x+\frac{b}{2}\) needs to be same.
That means.....
\(\frac{b}{2}=-4\\ \\ b=2(-4)\\ \\ b=-8\)
So, the value of \(b\) will be -8.
