To determine how many solutions the linear system has, we first need to analyze the equations given. The equations seem to be linear, but let’s clarify the system.
If we assume that the equations are meant to be:
- 6x + 2 = 0
- 12x + 2y = 4
We can rearrange these equations to find the values of x and y.
Starting with the first equation:
6x + 2 = 0
We can isolate x:
6x = -2
x = -1/3
Now, using the value of x we found in the second equation:
12(-1/3) + 2y = 4
This simplifies to:
-4 + 2y = 4
2y = 8
y = 4
We found a specific solution, (x, y) = (-1/3, 4). Since we obtained one unique solution by solving the linear equations, we can conclude that this linear system has exactly one solution.
In summary, the system has one unique solution, which is derived directly from solving the given linear equations.