determine whether the system of linear equations has one solution, infinitely many solutions, or no solutions. Explain your reasoning. y=4x+6, 2y=8x+12

Infinitely many solutions

Step-by-step explanation:

Since you already have y isolated in one equation, you can plug it in and use it in the other equation

2y = 8x + 12

2(4x + 6) = 8x + 12

8x + 12 = 8x + 12

Get the x's to one side

12 = 12

Meaning you have infinitely many solutions.

Try plugging in any x value you can think of and the left side will always equal the right side. so

x = 0 --> 8(0) + 12 = 8(0) + 12

12 =12

x = 1 --> 8(1) + 12 = 8(1) + 12

20 = 20

and so on.

I graphed it here for you and the 2 functions are on top of each other which means at every x value y = 4x + 6 is equal to 2y = 8x + 12