The solution that can be used to fill in both blanks in the table is (-8,5).
the correct answer is (-8,5)
First, let's solve the first equation, 2x - 2y = 6, for x:
2x = 2y + 6
x = (2y + 6)/2
x = y + 3
Next, substitute this value of x into the second equation, 4x + 4y = 28:
4(y + 3) + 4y = 28
4y + 12 + 4y = 28
8y + 12 = 28
8y = 16
y = 16/8
y = 2
Now, substitute the value of y into the equation x = y + 3:
x = 2 + 3
x = 5
Therefore, the solution to the system of equations is (x, y) = (5, 2).
This solution satisfies both equations:
2(5) - 2(2) = 6, and
4(5) + 4(2) = 28.
