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I see that people are posting E so maybe I am missing something but I liked option C. Since we need a value for X, each statement alone will be insufficient since they each have 2 variables and you cannot get 1 of them to a single value. Since each statement only has 2 variables and they are x and y, we can combine them to get a value for x. Answer C!

Eq 1 and 2 are insuff alone as they inclide two variables and its impossible to solve for one variable i.e x. Combined they provide the same info, so nothing new. Answer should be E.

Statement 1: 2x - 5y + 6 = 12 Subtract 6 from both sides to get: 2x - 5y = 6 Since we have one equation with 2 variables, there are infinitely many solutions. In other words, x can have infinitely many values, which means statement 1 is NOT SUFFICIENT.

ASIDE: If you're not 100% convinced that there are infinitely many solutions, you can always test some values There are several values of x and y that satisfy the equation 2x - 5y = 6. Here are two: Case a: x = 3 and y = 0, in which case x = 3 Case b: x = 8 and y = 2, in which case x = 8

Statement 2: 8x - (4x + 10y) + 27 = 39 Subtract 27 from both sides to get: 8x - (4x + 10y) = 12 Expand: 8x - 4x - 10y = 12 Simplify: 4x - 10y = 12 Here we have another equation with 2 variables, which means there are infinitely many solutions. In other words, x can have infinitely many values, which means statement 2 is NOT SUFFICIENT.

Statements 1 and 2 combined Statement 1 tells us that 2x - 5y = 6 Statement 2 tells us that 4x - 10y = 12 IMPORTANT: the two equations above are EQUIVALENT equations. If we take the equation 4x - 10y = 12 and divide both sides by 2 we get the EQUIVALENT equation 2x - 5y = 6 Since the two statements provide the same information, and since each statement alone is NOT SUFFICIENT, we can conclude that the COMBIEND statements are NOT SUFFICIENT

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