Question

A teacher wrote the equation 3y + 12 = 6x on the board. For what value of b would the additional equation 2y = 4x + b form a system of linear equations with infinitely many solutions?

Answer 1

3y + 12 = 6x
3y = 6x - 12
y = 2x - 4

2y = 4x + (-8)
y = 2x + (-4)....the same as y = 2x - 4

b would have to be a -8

Answer 2

The value of
`b` will be -8.

Explanation:

The two given equations are.....

`3y+12=6x...........................(1)\\ \\ 2y=4x+b.............................(2)`

From equation (1), we will get......

`3y=6x-12\\ \\ (3y)/(3)=(6x-12)/(3)\\ \\ y=2x-4`

From equation (2), we will get.....

`2y=4x+b\\ \\ (2y)/(2)=(4x+b)/(2)\\ \\ y=2x+(b)/(2)`

For getting the solution of the system as "infinitely many solutions" , both equations
`y=2x-4` and
`y=2x+(b)/(2)` needs to be same.

That means.....

`(b)/(2)=-4\\ \\ b=2(-4)\\ \\ b=-8`

So, the value of
`b` will be -8.