y = 4x y = x 2 − 12 A solution to the given system of equations is (x, y), where x 0. What is the value of x ?

Question

y = 4x y = x 2 − 12 A solution to the given system of equations is (x, y), where x > 0. What is the value of x ?

Accepted Answer

The correct answer is 6. It’s given that y = 4x and y = x 2 − 12. Since y = 4x, substituting 4x for y in the second equation of the given system yields 4x = x 2 − 12. Subtracting 4x from both sides of this equation yields 0 = x 2 − 4x − 12. This equation can be rewritten as 0 = (x − 6)(x + 2). By the zero product property, x − 6 = 0 or x + 2 = 0. Adding 6 to both sides of the equation x − 6 = 0 yields x = 6. Subtracting 2 from both sides of the equation x + 2 = 0 yields x = −2. Therefore, solutions to the given system of equations occur when x = 6 and when x = −2. It’s given that a solution to the given system of equations is (x, y), where x > 0. Since 6 is greater than 0, it follows that the value of x is 6.

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