How many solutions does this system of equations have? Explain how you know.

8x - 2y = -4
12x + 6 = 3y
8x - 2y = -4
12x + 6 = 3y
The system of equations have infinitely many solutions. This is because when we solve these pair of linear equations we get 0 = 0.
Let us see how!
8x - 2y = -4 \rightarrow equation 1
Writing this in the standard from y = mx +b we get
-2y = -8x -4
Dividing this by -2, the equation 1 becomes
y = 4x +2
12x + 6 = 3y \rightarrow equation 2
Writing this in standard form y = mx + b we get
-3y = -12x -6
Dividing this by -3, the equation 2 becomes
y = 4x + 2
Both equations are identical to each other, so when we equate them across each other to solve them we get,
4x + 2 = 4x + 2
\Rightarrow 0 = 0
This means that the system of equations have infinitely many solutions. Graphing such a system of linear equations on the axis gives us only one straight line.