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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.
Amy is creating beaded jewelry to give to her family and friends. For her family, she assembled 1 necklace, using a total of 60 beads. For her friends, she assembled 4 bracelets and 1 necklace, using a total of 100 beads. Assuming she uses a consistent number of beads for every bracelet and necklace, how many beads is she using for each?
Amy uses $---- beads for each bracelet and $---- beads for each necklace.
P.S. The answer is written as a value meaning would beads for bracelet and would be beads for necklace.
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1 solution
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.
Before you can solve, you must write a system of equations. Let x = the number of beads Amy uses to make a bracelet, and let y = the number of beads Amy uses to make a necklace.
y = 60 4x + y = 100
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.
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 10 0 1 60
The solution is (10, 60).
Amy uses 10 beads for each bracelet and 60 beads for each necklace.