Which of the following terms will make the systems equivalent?
A. 12x + 12y = 24
B. -14x - 8y = 8
C. -14x - 8y = -8
D. -12x - 12y = 24
The systems will be equivalent if the corresponding equations in the two systems have the same coefficients.
Looking at the first equation in each system:
A. 12x + 12y = 24
B. -14x - 8y = 8
C. -14x - 8y = -8
D. -12x - 12y = 24
From A, we can see that the coefficient of x is 12 and the coefficient of y is 12.
Comparing this with the other equations:
B. -14x - 8y = 8 has a different coefficient of x (-14) and a different coefficient of y (-8).
C. -14x - 8y = -8 has a different coefficient of x (-14) and a different coefficient of y (-8).
D. -12x - 12y = 24 has a different coefficient of x (-12) and a different coefficient of y (-12).
Therefore, the answer is A. 12x + 12y = 24, as it has the same coefficients for x and y as the first equation in the original system.