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Given that (x - 3)2 + (y + 4)2 = 25 and y = |x - 2|, what is a possible value of y?
aris solution:
The problem presents a system of 2 equations for 2 variables. The first is the equation of a circle, the second is an absolute value function. A circle and the “V” shape of absolute value may intersect at 0, 1, 2, 3, or 4 distinct points. By inspection, we can eliminate choices A and B, because y equals an absolute value expression and therefore cannot be negative. It’s fairly easy to test the remaining choices by plugging them in. If y = 1, then x = 1 or x = 3 according to the absolute value function. Plugging y = 1 and x = 1 into the circle equation creates a false statement, but plugging y = 1 and x = 3 into the circle equation creates a true statement, so 1 is a possible value for y.
i don't understand how you have four distinct interceptions or even how you can come to that conclusion.
aris solution:
The problem presents a system of 2 equations for 2 variables. The first is the equation of a circle, the second is an absolute value function. A circle and the “V” shape of absolute value may intersect at 0, 1, 2, 3, or 4 distinct points. By inspection, we can eliminate choices A and B, because y equals an absolute value expression and therefore cannot be negative. It’s fairly easy to test the remaining choices by plugging them in. If y = 1, then x = 1 or x = 3 according to the absolute value function. Plugging y = 1 and x = 1 into the circle equation creates a false statement, but plugging y = 1 and x = 3 into the circle equation creates a true statement, so 1 is a possible value for y.
i don't understand how you have four distinct interceptions or even how you can come to that conclusion.
