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Write a system of equations for the problem: The sum of two numbers is 33. The larger number is 3 more than two times the smaller number. What are the numbers?

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2 Answers

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.
Hi Lisa;
smaller...x
larger...2x+3
(x)+(2x+3)=33
x+2x+3=33
3x+3=33
Let's subtract 3 from both sides...
-3+3x+3=33-3
3x=30
Let's divide both sides by 3...
(3x)/3=30/3
x=10...smaller
2x+3=[(2)(10)]+3=20+3=23...larger
Let's check our work...
10+23=33