To find the same solution for both systems, we need to find the values of x and y that satisfy both equations in each system.
For the first system:
4x + y = -1
x + y = 2
We can solve this system by subtracting the second equation from the first equation:
(4x + y) - (x + y) = (-1) - (2)
3x = -3
x = -1
Substituting x = -1 into the second equation:
(-1) + y = 2
y = 3
So the solution for the first system is x = -1 and y = 3.
Now let's find the values of x and y for the second system:
8x + 2y = -2
-4x + cy = -8
Again, we can solve this system by subtracting the second equation from the first equation:
(8x + 2y) - (-4x + cy) = (-2) - (-8)
12x + (2 - cy) = 6
12x + 2 - cy = 6
12x - cy = 4
Now we need the same values of x and y that satisfy both equations:
-1 = 12*(-1) - 3c
-1 = -12 - 3c
11 = 3c
c = 11/3
Therefore, the value of c that would give the same solution for both systems is c = 11/3.