The sum of liz's and melinda's ages is 28. if liz was 1/3 melinda's age 6 years ago, how old will liz be next year?

The first thing we must do for this case is to define variables:
 We have then:
 x: liz's age
 y: melinda's age
 We now write the system of equations:
 
 By solving the system graphically we have that the age of each one is currently:
 
 Next year, the age of liz is:
 
 
 Next year, Liz's age is 11 years.
 Note: see attached image for the graphic solution.