y = x - 2 x + 4 y = 6 x - 12 Which ordered pair x , y

Question

y = x - 2 x + 4 y = 6 x - 12 Which ordered pair x , y is the solution to the given system of equations?

Accepted Answer

Choice C is correct. The second equation in the given system of equations is y = 6 x - 12 . Substituting 6 x - 12 for y in the first equation of the given system yields 6 x - 12 = x - 2 x + 4 . Factoring 6 out of the left-hand side of this equation yields 6 x - 2 = x - 2 x + 4 . An expression with a factor of the form x - a is equal to zero when x = a . Each side of this equation has a factor of x - 2 , so each side of the equation is equal to zero when x = 2 . Substituting 2 for x into the equation 6 x - 2 = x - 2 x + 4 yields 6 2 - 2 = 2 - 2 2 + 4 , or 0 = 0 , which is true. Substituting 2 for x into the second equation in the given system of equations yields y = 6 2 - 12 , or y = 0 . Therefore, the solution to the system of equations is the ordered pair 2 , 0 . Choice A is incorrect and may result from switching the order of the solutions for x and y . Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Question y-x-2-