`x+y=0`
`3x-2y=10`
Which of the following ordered pairs (x y) satisfies the system of equations above?

Options

A. (3, −2)
B. (2, −2)
C. (−2, 2)
D. (−2, −2)

Explanation

Choice B is correct. Multiplying each side of x + y = 0 by 2 gives 2x + 2y = 0. Then, adding the corresponding sides of 2x + 2y = 0 and 3x − 2y = 10 gives 5x = 10. Dividing each side of 5x = 10 by 5 gives x = 2. Finally, substituting 2 for x in x + y = 0 gives 2 + y = 0, or y = −2. Therefore, the solution to the given system of equations is (2, −2).
Alternatively, the equation x + y = 0 can be rewritten as x = -y, and substituting x for −y in 3x − 2y = 10 gives 5x = 10, or x = 2. The value of y can then be found in the same way as before.
Choices A, C, and D are incorrect because when the given values of x and y are substituted into x + y = 0 and 3x − 2y = 10, either one or both of the equations are not true. These answers may result from sign errors or other computational errors.