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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineA baseball coach takes his team out for pizza every time they win a game. Not everyone can come each time, so he orders the pizzas based on how many players are coming. After last week's victory, he bought 11 large pizza, the perfect amount for the 55 players going out for pizza. This week, there were 3030 players going, so he ordered 55 small pizzas and 55 large pizzas, which was also just the right amount. How many people does each size of pizza feed?\newlineEach small pizza feeds ____\_\_\_\_ people, and each large pizza feeds ____\_\_\_\_ people.

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Q. Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineA baseball coach takes his team out for pizza every time they win a game. Not everyone can come each time, so he orders the pizzas based on how many players are coming. After last week's victory, he bought 11 large pizza, the perfect amount for the 55 players going out for pizza. This week, there were 3030 players going, so he ordered 55 small pizzas and 55 large pizzas, which was also just the right amount. How many people does each size of pizza feed?\newlineEach small pizza feeds ____\_\_\_\_ people, and each large pizza feeds ____\_\_\_\_ people.
  1. Set Equations: Let's call the number of people a small pizza feeds ss and the number of people a large pizza feeds ll. From the first scenario, we have the equation:\newline1l=51l = 5
  2. Create Augmented Matrix: From the second scenario, we have the equation: 5s+5l=305s + 5l = 30
  3. Perform Elimination: Now we have a system of equations:\newline1l=51l = 5\newline5s+5l=305s + 5l = 30\newlineWe can represent this system as an augmented matrix.
  4. Solve for ss: The augmented matrix is: [0amp;1∣amp;5 5amp;5∣amp;30]\begin{bmatrix} 0 & 1 | & 5 \ 5 & 5 | & 30 \end{bmatrix}
  5. Solve for ss: The augmented matrix is:\newline\begin{array}{cc|c} 0 & 1 & 5 \ 5 & 5 & 30 \end{array}First, let's multiply the first row by 55 to use it for elimination in the second row.\newline\begin{array}{cc|c} 0 & 5 & 25 \ 5 & 5 & 30 \end{array}
  6. Solve for s: The augmented matrix is:\newline\begin{array}{cc|c} 0 & 1 & 5 \ 5 & 5 & 30 \end{array}First, let's multiply the first row by 55 to use it for elimination in the second row.\newline\begin{array}{cc|c} 0 & 5 & 25 \ 5 & 5 & 30 \end{array}Now, subtract the first row from the second row to eliminate ll and solve for ss.\newline\begin{array}{cc|c} 0 & 5 & 25 \ 5 & 0 & 5 \end{array}

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