OG详解-OG5 数学1 Q13

The correct answer is 6. It’s given that y = 4x and y = x² - 12. Since y = 4x, substituting 4x for y in the second equation of the given system yields 4x = x² -12. Subtracting 4x from both sides of this equation yields 0 = x² -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.