LINEAR SYSTEMS Solving a word problem involving a sum and another basic... The sum of two numbers is 51 . The smaller number is 15 less than the larger number. What are the numbers? Larger number: Smaller number:

Step 1 ：Set up the equations: \(x + y = 51\) and \(y = x - 15\)

Step 2 ：Substitute the second equation into the first: \(x + (x - 15) = 51\)

Step 3 ：Solve for x: \(2x - 15 = 51\) => \(2x = 66\) => \(x = 33\)

Step 4 ：Substitute x back into the second equation: \(y = 33 - 15\) => \(y = 18\)

Step 5 ：\(\boxed{\text{Larger number: 33}}\)

Step 6 ：\(\boxed{\text{Smaller number: 18}}\)