y = 4 x y = x 2 - 12 A solution to the given system of equations is x

Question

y = 4 x y = x 2 - 12 A solution to the given system of equations is x , y , where x &#62; 0 . What is the value of x ?

Accepted Answer

The correct answer is 6 . It&rsquo;s given that y = 4 x and y = x 2 - 12 . Since y = 4 x , substituting 4 x for y in the second equation of the given system yields 4 x = x 2 - 12 . Subtracting 4 x from both sides of this equation yields 0 = x 2 - 4 x - 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&rsquo;s given that a solution to the given system of equations is x , y , where x &#62; 0 . Since 6 is greater than 0 , it follows that the value of x is 6 .

Question y-4-x-