To solve the system of equations, we have the following two equations:
- \( 4h + 4s = 10 \)
- \( 7h + 5s = 15 \)
We can simplify the first equation by dividing all terms by 4:
\[ h + s = 2.5 \quad (1) \]
Next, we'll express \( s \) in terms of \( h \) from equation (1):
\[ s = 2.5 - h \quad (2) \]
Now we'll substitute equation (2) into the second equation:
\[ 7h + 5(2.5 - h) = 15 \]
This expands to:
\[ 7h + 12.5 - 5h = 15 \]
Combining like terms gives:
\[ 2h + 12.5 = 15 \]
Now, subtract 12.5 from both sides:
\[ 2h = 15 - 12.5 \] \[ 2h = 2.5 \]
Dividing both sides by 2:
\[ h = 1.25 \]
Now, we can substitute \( h \) back into equation (2) to find \( s \):
\[ s = 2.5 - 1.25 \] \[ s = 1.25 \]
Thus, the solution is: \[ h = 1.25 \quad \text{(cost of a hot dog)} \] \[ s = 1.25 \quad \text{(cost of a soda)} \]
So, the cost of both the hot dog and the soda is $1.25.