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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.Mario's Pizza just received two big orders from customers throwing parties. The first customer, Ruth, bought deluxe pizza and paid . The second customer, Gordon, ordered regular pizzas and deluxe pizzas, paying a total of . What is the price of each pizza?Each regular pizza costs _____, and each deluxe pizza costs ______.
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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.Mario's Pizza just received two big orders from customers throwing parties. The first customer, Ruth, bought deluxe pizza and paid . The second customer, Gordon, ordered regular pizzas and deluxe pizzas, paying a total of . What is the price of each pizza?Each regular pizza costs _____, and each deluxe pizza costs ______.
- Define Variables: Let be the cost of a regular pizza and be the cost of a deluxe pizza. Ruth's order gives us the equation: .
- Equations from Orders: Gordon's order gives us the equation: .
- System of Equations: We now have the system of equations:. .
- Augmented Matrix: To solve using an augmented matrix, we rewrite the system as:\begin{bmatrix}0 & 1 & | & 22\9 & 3 & | & 174\end{bmatrix}
- Eliminate Variable : We need to eliminate from the second equation. To do this, we can multiply the first equation by and add it to the second equation.
- Multiply and Add: Multiplying the first equation by gives us:
- New Second Equation: Adding this to the second equation:This should give us a new second equation.
