Identify the variables and write a system of equations for the story problem.

Step 1, label variables.

x=larger number

y=smaller number

Step 2, Convert sentences into equations

The sum of 2 numbers is 33.

x + y = 33

The larger number (x) is 3 more than 2 times the smaller number (y)

x = 2y + 3

Step 3: Substitute second equation into first equation and solve for y.

(2y + 3) + y = 33

3y + 3 -3 = 33 -3

3y/3 = 30/3

y = 10

Step 4: Substitute solved value for y and solve for x

x = 2y + 3

x = 2(10) + 3

x = 20 + 3 = 23

Step 5: Check x+y=33, 23 + 10 = 33 Check.