The sum of two numbers is 65. The difference of the two numbers is 27. Write and solve a system of linear equations to find the two numbers. Let x represent the greater number,and let y represent the lesser number.

x + y = 65 The sum of two numbers (x and y) is 65
x - y = 27 The difference of the two numbers is 27

This can easily be solved with elimination.

2x = 92
x = 46

Then we solve for y replacing the x value for x.
46 + y = 65
y = 19

The solution is (46, 19).

If you want substitution:

x + y = 65
x - y = 27

y = 65 - x
x - y = 27

x - (65 - x) = 27
x - 65 + x = 27
2x - 65 = 27
2x = 92
x = 46

Then solve for y using either equation.
46 - y = 27
- y = - 19
y = 19

We get the same solution (46, 19). You can check this by plugging in the x and y values into one or both equations.