To solve the system of linear equations:
- \( 4h + 4s = 10 \) (Equation 1)
- \( 7h + 5s = 15 \) (Equation 2)
we can start by simplifying Equation 1. Dividing the entire equation by 4 gives us:
\[ h + s = 2.5 \quad (Equation 1') \]
Now we can express \( s \) in terms of \( h \):
\[ s = 2.5 - h \]
Next, we can substitute \( s \) from Equation 1' into Equation 2:
\[ 7h + 5(2.5 - h) = 15 \]
Distributing the 5:
\[ 7h + 12.5 - 5h = 15 \]
Combining like terms:
\[ 2h + 12.5 = 15 \]
Now, subtract 12.5 from both sides:
\[ 2h = 2.5 \]
Dividing both sides by 2 gives:
\[ h = 1.25 \]
Now, substitute \( h \) back into the equation for \( s \):
\[ s = 2.5 - 1.25 = 1.25 \]
Thus, the solutions are:
\[ h = 1.25 \quad (cost \text{ of a hot dog}) \] \[ s = 1.25 \quad (cost \text{ of a soda}) \]
In decimal form, the final answers are:
\( h = 1.25 \)
\( s = 1.25 \)
1 answer