Part 1: The linear equations are [tex]m=3+9j[/tex] and [tex]3j-m+27=0[/tex]
Part 2: Solving the equations, we have, [tex]j=4[/tex] and [tex]m=40[/tex]
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,
[tex]m=3+9j[/tex]
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,
[tex](m+11)=5+3(j+11)[/tex]
Simplifying this, we get,
[tex]m+11=5+3j+33\\m+11=3j+38[/tex]
Thus, the linear equation is
[tex]3j-m+27=0[/tex]
The linear equations are [tex]m=3+9j[/tex] and [tex]3j-m+27=0[/tex]
Part 2: Solving the linear equation, we get,
Substituting [tex]m=3+9j[/tex] in [tex]3j-m+27=0[/tex]
[tex]3j-3-9j+27=0\\[/tex]
Simplifying, we get,
[tex]-6j=-24[/tex]
Hence, [tex]j=4[/tex]
Substituting [tex]j=4[/tex] in [tex]m=3+9j[/tex]
[tex]m=3+9(4)\\m=3+36\\m=40[/tex]
Solving the equations, we have, [tex]j=4[/tex] and [tex]m=40[/tex]
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.
