Currently, Jacob's mother is three more than nine times as old as Jacob. In eleven years, his mother will be five more than three times his age.

Part 1: Write a system of linear equations that models this situation. Let j represent Jacob's age, and let m represent his mother's age.

Part 2:Solve the system of equations
Part 3:complete the sentence.
Jacob isyears old and his mother is years old.

Part 1: The linear equations are and

Part 2: Solving the equations, we have, and

Part 3: Jacob is 4 years old and his mother is 40 years old.

Explanation:

Part 1: Let j represent Jacob's age, and let m represent his mother's age.

It is given that, "Jacob's mother is three more than nine times as old as Jacob". Writing it as linear equation, we have,

It is also given that, "In eleven years, his mother will be five more than three times his age". Writing it as linear equation, we have,

Simplifying this, we get,

Thus, the linear equation is

The linear equations are   and

Part 2: Solving the linear equation, we get,

Substituting in

Simplifying, we get,

Hence,

Substituting in

Solving the equations, we have, and

Part 3: Since, j represents jacob and m represents the jacob's mother

Thus, Jacob is 4 years old and his mother is 40 years old.