One number is 6 more than twice another. if their sum is 51, find the numbers. which of the following systems of equations represents the word problem?

a. y = 2x + 6 and y = x + 51
b. = 2x + 6 and x + y = 51
c. y = 2(x + 6) and x + y = 51

Let x and y be the two unknown numbers. The first statement says that one number say x, is 6 more than twice another, say, y. If we express this mathematically, that would be:

x = 6 + 2y   or that could be   y = 6 + 2x

The second statement says that the sum of both numbers, x and y, is 51. That would be

x + y = 51

From the choices, the answer would be
B. y = 2x + 6 and x + y = 51

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