x=y-3
`x/2+2y=6`
Which ordered pair (x, y) satisfies the system of equations shown above?

Options

A. ( −3, 0)
B. (0, 3)
C. (6, −3)
D. (36, −6)

Answer

B

Explanation

Choice B is correct. The first equation can be rewritten as y – x = 3 and the second as `x/4+y =3` , which implies that `-x=x/4`, and so x=0. _ 4 + y = 3, which implies that −x = x _ 4 , and so x = 0. The ordered pair (0, 3) satisfies the first equation and also the second, since 0 + 2(3) = 6 is a true equality. Alternatively, the first equation can be rewritten as y = x + 3.
Substituting x + 3 for y in the second equation gives `x/2 + 2(x + 3) = 6`.
This can be rewritten using the distributive property as `x/2` + 2x + 6 = 6. It follows that 2x + `x/2` must be 0. Thus, x = 0. Substituting 0 for x in the equation y = x + 3 gives y = 3. Therefore, the ordered pair (0, 3) is the solution to the system of equations shown. Choice A is incorrect, it satisfies the first equation but not the second. Choices C and D are incorrect because neither satisfies the first equation, x = y − 3.