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