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

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.

Answer 2

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