let x be the age of Amelia, and y the age of Taylor.
[tex]x+y=30[/tex]
[tex]x-10=3y[/tex]
We can simplify the second equation to get:
[tex]x+y=30[/tex]
[tex]x-3y=10[/tex]
We can solve for x in the first equation to get:
[tex]x=30-y[/tex]
Now we can replace this into our second equation to get:
[tex]30-y-3y=10[/tex]
[tex]30-4y=10[/tex]
[tex]-4y=-20[/tex]
[tex]y= \frac{-20}{-4} [/tex]
[tex]y=5[/tex]
Now know that the age of Taylor is 5 years, let's find the age of Amelia replacing this value into our equation [tex]x=30-y[/tex]
[tex]x=30-5[/tex]
[tex]x=25[/tex]
We conclude that the age of Amelia is 25 year old and Taylor is 5 years old.
