Answer:

Lian is 12 years old and Ella is 8 years old.

Step-by-step explanation:

Lian and her younger sister Ella are 4 years apart.

The sum of their ages is 20.

Let L be Lian’s age in years.

Let E be Ella’s age in years.

The system of linear equations that models the scenario is:

L-4=E this gives L=E+4

L+E=20

Putting L=E+4 in the second equation

E+4+E=20

2E=20-4

2E=16

So, E=8

Now we have , L+E=20

L+8=20

So, L=12

Therefore, Lian is 12 years old and Ella is 8 years old.