The difference of two numbers is 17. Find the numbers if twice the smaller plus three times the larger is 66. Number Problems: Answer: The two numbers are 20 and 3 . Step-by-step explanation: To find for the two numbers, let x be the larger number and y be the smaller number then x - y = 17 and 3x + 2y = 66. In order to apply the elimination method, multiply x - y = 17 by 2 such that 2(x - y = 17) which will give 2x - 2y = 34. Add 2x - 2y = 34 to 3x + 2y = 66 to eliminate y and solve for x such that 2x + 3x = 5x, -2y + 2y = 0, 34 + 66 = 100 then 5x = 100. Divide both sides of the equation by 5 thus, x = 20 . If the larger number is 20 then use x - y = 17 such that 20 - y = 17, -y = 17 - 20, -y = -3. To remove the negative sign of y multiply both sides of the equation by -1 such that -1(-y = -3) thus, y = 3 . To check whether the obtained numbers are correct, use x - y = 17 then 20 - 3 = 17, 17 = 17 or 3x + 2y = 66, 3(20) + 2(3) = 66, 60 + 6 = 66, 66 = 66. Read more on brainly.p...