How many solutions does the system have?

Question

6x - y = -1
6x + y = -1

Answer 1

The two equations in the system are:

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

To determine the number of solutions, we can try to eliminate one of the variables. Adding equation 1) and equation 2), we get:

(6x - y) + (6x + y) = -1 + (-1)
12x = -2
x = -2/12
x = -1/6

Now we can substitute the value of x into one of the equations to solve for y. Let's use equation 1):

6(-1/6) - y = -1
-1 - y = -1
y = 0

Therefore, the system has one unique solution, where x = -1/6 and y = 0.