How many solutions does this linear system have? Y=-6x+2 and - 12x-2y=-4

We can solve the system of equations to check the number of system of the solutions.

y=-6x+2 ... (1)

-12x-2y=-4 ... (2)

Substitute - 6x+2 for y in equation (2). So,

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

-12x+12x-4=-4 (By distribution property).

-4=-4 (-12x and + 12x has been cancel out).

Notice x has vanish from the above equation and we are left with - 4=-4 which is correct.

So, the system has infinte number of solutions.