\(x-\ Karen's\ age\\\\
y-\ Suzanne's\ age\\\\
\left \{ {{x=y+7} \atop {x-4=2(y-4)}} \right.\\\\ \left \{ {{x=y+7} \atop {x-4=2y-8}} \right.\\\\ \left \{ {{x=y+7} \atop {x=2y-4}} \right.\\\\y+7=2y-4\ \ \ | subtract\ 2y\\\\
-y+7=-4\ \ \ | subtract\ 7\\\\
-y=-11\ \ \ | multiply\ by\ -1\\\\
y=11\\\\
x=11+7=18\\\\
Now\ Karen\ is\ 18\ years\ old \ and\ Suzanne\ is\ 11\ years\ old.\)
