The booster club is selling refreshments. The following system of linear equations models the concession stand prices. Let represent the cost of a hot dog and represent the cost of the soda. Write the answers in decimal form. Solve the system of linear equations.4h+4s=107h+5s=15(1 point)h=$s=$

Answer 1

To solve the system of linear equations given by:

1. \( 4h + 4s = 107 \)
2. \( 7h + 5s = 15 \)

let's first simplify the first equation by dividing everything by 4:

\[ h + s = 26.75 \quad \text{(Equation 1)} \]

Now we have:

1. \( h + s = 26.75 \)
2. \( 7h + 5s = 15 \)

We can express \( s \) in terms of \( h \) from Equation 1:

\[ s = 26.75 - h \quad \text{(Equation 2)} \]

Now we will substitute Equation 2 into the second equation:

\[ 7h + 5(26.75 - h) = 15 \]

Distributing the 5:

\[ 7h + 133.75 - 5h = 15 \]

Now combine like terms:

\[ 2h + 133.75 = 15 \]

Subtract 133.75 from both sides:

\[ 2h = 15 - 133.75 \] \[ 2h = -118.75 \]

Now, divide by 2:

\[ h = -59.375 \]

Now substitute \( h \) back into Equation 2 to find \( s \):

\[ s = 26.75 - (-59.375) \] \[ s = 26.75 + 59.375 \] \[ s = 86.125 \]

So the solutions are:

\[ h = -59.375, \quad s = 86.125 \]

However, negative prices do not make sense in this context. There may have been a mistake in the interpretation or constraints of the equations provided. Please double-check the original equations for any errors.