let

p = the age of Peggy

r =the age of Rosa

Peggy is 6 years older than rosa

p = 6 + r

Two years from now Peggy will be twice as old as rosa

2 + p = 2(r + 2)

by solving the system of equations

p = 6 + r

2 + p = 2(r + 2)

we find

p = 10 years

r = 4 years

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Peggy is 10 years old.

Rosa is 4 years old.