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x = y - 3
x/2 + 2y = 6
Which ordered pair (x, y) satisfies the system of equations shown above?
  • a)
    (−3, 0)
  • b)
    (0, 3)
  • c)
    (6, − 3)
  • d)
    (36, − 6)
Correct answer is option 'B'. Can you explain this answer?
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x = y - 3x/2 + 2y = 6Which ordered pair (x, y) satisfies the system of...
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 = _x4, 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.
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x = y - 3x/2 + 2y = 6Which ordered pair (x, y) satisfies the system of equations shown above?a)(−3, 0)b)(0, 3)c)(6, − 3)d)(36, − 6)Correct answer is option 'B'. Can you explain this answer?
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