Short Answer 
The balance equation defines relationships between shapes, where a triangle plus a star equals a hexagon (T + S = H). By substituting H in a new expression H + S, we find it balances to T + 2S, illustrating that one hexagon and one star equate to one triangle and two stars.
Step 1: Understand the Balance Equation
In a balance, both sides must have equal values. To interpret the given relationship, we define symbols for the shapes: T for triangle, S for star, and H for hexagon. The initial relationship presented is:
- T + S = H
This means the value of a triangle plus a star equals the value of a hexagon.
Step 2: Substitute Values to Find New Equations
To explore further, we want to determine how we can balance a new expression: H + S. To do this, we use our earlier equation to substitute H. This results in:
- H + S = T + S + S
This shows that one hexagon plus one star can be balanced by one triangle and two stars.
Step 3: Identify the Respective Shapes
Now, we need to determine how many of each shape corresponds to the new equation. The expression T + S + S indicates the presence of:
- 1 triangle (T)
- 2 stars (S)
This representation ultimately helps us visualize that the configuration with one triangle and two stars matches the condition set by our balance equation.