If x is the tens digit and y is the ones digit, which system of equations represents the word problem?

Question

The sum of the digits of a two digit number is 14. The difference between the tens digit and the units digit is 2. If x is the tens digit and y is the ones digit, which system of equations represents the word problem?

Answer 1

Start by breaking down the first sentence. "The sum of digits of a two digit number is 14." They key words from that are sum, two digit, and 14. Sum is the answer to an addition problem, so we know we are adding. We know that it's a two digit number, so that eliminates anything 9 and under and anything 100 or higher. And we know that if the individual digits are added together we get 14. Later on it says that x will stand for the tens digit and y will stand for the one digit. So, putting it all together will get us x + y = 14.

 

The second sentence "The difference between the tens digit and the units digit is 2." Difference = subtraction. The answer to that subtraction problem will be 2. And we know its the tens digit minus the ones, and as we said earlier the tens digit is x and the units digit is y, so x - y = 2

 

Now, we have our system of equations. All we did was take the words and translate into numbers and symbols. You have all you need to solve for x and y if that is needed by using elimination.  

 

x + y = 14

x -  y = 2

Answer 2

xy

 

x+y=14

x-y=2

 

if you solve the system, you get 86 for the number