To solve the system of linear equations given by:
- \( 4h + 4s = 10 \) (Equation 1)
- \( 7h + 5s = 15 \) (Equation 2)
we can start by simplifying Equation 1:
\[ 4h + 4s = 10 \] Dividing the entire equation by 4 gives:
\[ h + s = 2.5 \quad (Equation 3) \]
Now, we can express \( s \) in terms of \( h \):
\[ s = 2.5 - h \quad (Equation 4) \]
Next, we substitute Equation 4 into Equation 2:
\[ 7h + 5(2.5 - h) = 15 \]
Distributing \( 5 \):
\[ 7h + 12.5 - 5h = 15 \]
Combining like terms gives:
\[ 2h + 12.5 = 15 \]
Subtracting \( 12.5 \) from both sides:
\[ 2h = 2.5 \]
Dividing by \( 2 \):
\[ h = 1.25 \]
Now, substitute \( h = 1.25 \) back into Equation 4 to find \( s \):
\[ s = 2.5 - 1.25 = 1.25 \]
Thus, the solution to the system is:
\[ h = 1.25 \] \[ s = 1.25 \]
The final answers in decimal form are:
\[ h = 1.25 \] \[ s = 1.25 \]
So, the cost of a hot dog, \( h \), is:
\[ \boxed{1.25} \]