To solve the system of linear equations given by:
1. \( 4h + 4s = 10 \) (Equation 1)
2. \( 7h + 5s = 15 \) (Equation 2)
We can start with Equation 1. We can simplify it by dividing everything by 4:
\[
h + s = 2.5 \quad (Equation 3)
\]
Now we can express \( s \) in terms of \( h \):
\[
s = 2.5 - h \quad (Equation 4)
\]
Next, we substitute Equation 4 into Equation 2:
\[
7h + 5(2.5 - h) = 15
\]
Now, distribute the 5:
\[
7h + 12.5 - 5h = 15
\]
Combine like terms:
\[
2h + 12.5 = 15
\]
Now, isolate \( h \):
\[
2h = 15 - 12.5
\]
\[
2h = 2.5
\]
\[
h = \frac{2.5}{2} = 1.25
\]
Now that we have \( h \), we can plug it back into Equation 4 to find \( s \):
\[
s = 2.5 - 1.25
\]
\[
s = 1.25
\]
So, the solution is:
\[
h = 1.25 \quad \text{(cost of a hot dog)}
\]
\[
s = 1.25 \quad \text{(cost of a soda)}
\]
Finally, in decimal form:
\[
h = \$1.25
\]
\[
s = \$1.25
\]