The booster club is selling refreshments. The following system of linear equations models the concession stand prices. Let h represent the cost of a hot dog and s represent the cost of the soda. Write the answers in decimal form. Solve the system of linear equations.

Answer 1

To solve the system of linear equations that models the concession stand prices, we'll need the specific equations that represent the problem. Since you haven't provided the equations, I can explain the general process of solving a system of linear equations.

Suppose the system of equations is represented as follows:

1. \( a_1h + b_1s = c_1 \)
2. \( a_2h + b_2s = c_2 \)

To solve this system using the substitution or elimination method, follow these steps:

Method 1: Substitution

1. Solve one of the equations for one variable in terms of the other.
2. Substitute this expression into the second equation.
3. Solve for the remaining variable.
4. Substitute back to find the value of the first variable.

Method 2: Elimination

1. Multiply each equation by suitable constants to align coefficients of one variable.
2. Add or subtract the equations to eliminate one variable.
3. Solve for the remaining variable.
4. Substitute back to find the first variable.

Example

Let's say we have the following equations:

1. \( 2h + 3s = 10 \)
2. \( 4h + s = 8 \)

Using elimination:

1. Multiply the second equation by 3 to align with the first equation: \[ 12h + 3s = 24 \]

2. Now we have: \[ 2h + 3s = 10 \] \[ 12h + 3s = 24 \]

3. Subtract the first equation from the second: \[ (12h + 3s) - (2h + 3s) = 24 - 10 \] \[ 10h = 14 \] \[ h = 1.4 \]

4. Substitute \( h = 1.4 \) back into one of the original equations to find \( s \): \[ 2(1.4) + 3s = 10 \] \[ 2.8 + 3s = 10 \] \[ 3s = 10 - 2.8 \] \[ 3s = 7.2 \] \[ s = 2.4 \]

Results

Thus, the solution would be:

• Cost of hot dog \( h = 1.4 \)
• Cost of soda \( s = 2.4 \)

If you have specific equations to work with, please provide them, and I can help solve that exact case!