Algebra 1 : How to find the solution for a system of equations
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Example Question #92 : Equations / Solution Sets
We have three dogs: Joule, Newton, and Toby. Joule is three years older than twice Newton's age. Newton is Toby's age younger than eleven years. Toby is one year younger than Joules age. Find the age of each dog.
Joule: 8 years
Newton: 4 years
Toby: 8 year
none of these
Joule: 12 years
Newton: 1 year
Toby: 5 year
Joule: 5 years
Newton: Not born yet
Toby: 1 year
Joule: 9 years
Newton: 3 years
Toby: 8 year
Joule: 9 years
Newton: 3 years
Toby: 8 year
First, translate the problem into three equations. The statement, "Joule is three years older than twice Newton's age" is mathematically translated as
where 
The statement, "Newton is Toby's age younger than eleven years" is translated as
where 
The third statement, "Toby is one year younger than Joule" is
So these are our three equations. To figure out the age of these dogs, first I will plug the third equation into the second equation. We get
Plug this equation into the first equation to get
Solve for 
Divide both sides by 3
So Joules is 9 years old. Plug this value into the third equation to find Toby's age
Toby is 8 years old. Use this value to find Newton's age using the second equation
Now, we have the age of the following dogs:
Joule: 9 years
Newton: 3 years
Toby: 8 years
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