5 x + 14 y = 45 10 x + 7 y = 27 The solution to the given system

Question

5 x + 14 y = 45 10 x + 7 y = 27 The solution to the given system of equations is x , y . What is the value of x y ?

Accepted Answer

The correct answer is 9 5 . Multiplying the first equation in the given system by 2 yields 10 x + 28 y = 90 . Subtracting the second equation in the given system, 10 x + 7 y = 27 , from 10 x + 28 y = 90 yields 10 x + 28 y - 10 x + 7 y = 90 - 27 , which is equivalent to 10 x + 28 y - 10 x - 7 y = 63 , or 21 y = 63 . Dividing both sides of this equation by 21 yields y = 3 . The value of x can be found by substituting 3 for y in either of the two given equations. Substituting 3 for y in the equation 10 x + 7 y = 27 yields 10 x + 7 3 = 27 , or 10 x + 21 = 27 . Subtracting 21 from both sides of this equation yields 10 x = 6 . Dividing both sides of this equation by 10 yields x = 6 10 , or x = 3 5 . Therefore, the value of x y is 3 5 3 , or 9 5 . Note that 9/5 and 1.8 are examples of ways to enter a correct answer.

Question 5-x-14