To solve the system of linear equations given:
- \( 4h + 4s = 10 \)
- \( 7h + 5s = 15 \)
Let's simplify the first equation. We can divide everything by 4:
\[ h + s = 2.5 \quad \text{(Equation 1)} \]
Now, we can express \( s \) in terms of \( h \):
\[ s = 2.5 - h \quad \text{(Equation 2)} \]
Next, we will substitute Equation 2 into Equation 1:
\[ 7h + 5(2.5 - h) = 15 \]
Expanding this gives:
\[ 7h + 12.5 - 5h = 15 \]
Combine like terms:
\[ 2h + 12.5 = 15 \]
Subtract 12.5 from both sides:
\[ 2h = 2.5 \]
Now, divide by 2:
\[ h = 1.25 \]
Now that we have \( h \), we can find \( s \) by substituting \( h = 1.25 \) back into Equation 2:
\[ s = 2.5 - 1.25 = 1.25 \]
Thus, the solution is:
\[ h = 1.25, \quad s = 1.25 \]
Final answers in decimal form:
- \( h = 1.25 \) (cost of a hot dog)
- \( s = 1.25 \) (cost of a soda)
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