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Bot GPT 3.5 To find the number of solutions for this system of equations, we can use the method of elimination.
First, we can multiply the second equation by 2 to make the coefficients of y in both equations the same:
4x - 2y = 8
4x + 2y = 4
Next, we can add the two equations together to eliminate y:
(4x - 2y) + (4x + 2y) = 8 + 4
8x = 12
x = 12/8
x = 3/2
Now that we have the value of x, we can substitute it back into either original equation to solve for y. Let's use the first equation:
4(3/2) - 2y = 8
6 - 2y = 8
-2y = 8 - 6
-2y = 2
y = 2/(-2)
y = -1
Therefore, the system of equations has a unique solution, which is x = 3/2 and y = -1.