IXL - Solve a system of equations using augmented matrices: word problems (Algebra 2 practice)

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, Zeke, bought 1 deluxe pizza and paid $23. The second customer, Jacob, ordered 9 regular pizzas and 5 deluxe pizzas, paying a total of $187. What is the price of each pizza?

Each regular pizza costs $, and each deluxe pizza costs $.

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Learn with an example

question

Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.

Mrs. Bowen is shopping for school supplies with her children. Hannah selected 1 two-inch binder, which cost a total of $9. Seth selected 4 one-inch binders and 5 two-inch binders, which cost a total of $61. How much does each size of binder cost?

A one-inch binder costs $, and a two-inch binder costs $.

key idea

To solve using augmented matrices, follow these three steps:

Step 1: Write the augmented matrix.

Step 2: Use elementary row operations to transform the left part of the augmented matrix into the identity matrix.

Step 3: State the solution.

solution

Before you can solve, you must write a system of equations. Let x represent the cost of a one-inch binder, and let y represent the cost of a two-inch binder.

y = 9

4x + 5y = 61

Now use augmented matrices to solve the system of equations.

Step 1: Write the augmented matrix.

Since both equations are in standard form, you can write the numbers in an augmented matrix.

0x + 1y = 9

4x + 5y = 61

→

0	1		9
4	5		61

Step 2: Use elementary row operations to transform the left part of the augmented matrix into the identity matrix.

There are three elementary row operations:

Swap any two rows

Multiply any row by a non-zero number

Add a multiple of any row to any other row

Use these three operations to make the part of the matrix to the left of the dashed line look like the identity matrix:

1	0
0	1

Start with the augmented matrix from Step 1.

0	1		9
4	5		61

4	5		61
0	1		9

Swap R₁ with R₂

Multiply R₁ by

1	0		4
0	1		9

Add

^–5

R₂

to R₁

The left part is now the identity matrix, so no more row operations need to be performed.

Step 3: State the solution.

The solution is the last column of the new matrix.

1	0		4
0	1		9

The solution is (4, 9).

A one-inch binder costs $4, and a two-inch binder costs $9.

Looking for more? Try this:

$Confetti$

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TT.18Solve a system of equations using augmented matrices

E.9Solve a system of equations using elimination: word problems

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