Trina planted 43 plants. she planted twice as many cucumbers as zucchini and eight more tomatoes than cucumbers. write and solve an equation to find the number of each kind of plant in her

To answer this question you can create an equation in terms of the number of zucchini that were planted.  Each other plant gives information that can relate to the number of zucchini plants.

# of cucumbers +   # of tomatoes  + # of zucchini
       2z              +           2z + 8     +       z =  43 
       5z + 8 = 43
             -8     -8
       5z      = 35
       5           5 
       z = 7 plants

There were 7 zucchini plants, 14 (2 x 7) cucumber plants, and 22 (2 x 7 + 8) tomato plants.      

z+c+t = 48, 7 zucchini, 14 Cucumbers, 22 tomatoes
In this equation, we will change all plants in terms of zucchini
zuccini=z (base term)
cucumbers =2z (two times the number of zucchini
tomatoes = 2z+8 (eight more than cucumbers)
z+c+t= 43
z+2z+2z+8=43 combine like terms
5z+8=43 subtract both sides by 8
5z=35 divide by 5
z=7
Plug in values for z to solve for c and t
cucumbers = 2(7) = 14
Tomatoes = 2(7)+8 = 22