The school band needs $500 to buy new hats. They already have $200. They are selling bumper stickers for 1.50 each. How many bum
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Answer:
The system has infinitely many solutions.
Step-by-step explanation:
To find the solution for this system of linear equations you must:
Step 1: Transform the augmented matrix to the reduced row echelon form.
A matrix is a rectangular arrangement of numbers into rows and columns.
A system of equations can be represented by an augmented matrix.
In an augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.
This is matrix that represents the system
The augmented matrix can be transformed by a sequence of elementary row operations to the matrix.
There are three kinds of elementary matrix operations.
- Interchange two rows (or columns).
- Multiply each element in a row (or column) by a non-zero number.
- Multiply a row (or column) by a non-zero number and add the result to another row (or column).
Using elementary matrix operations, we get that
Row Operation 1: Multiply the 1st row by -1/3
Row Operation 2: Multiply the 2nd row by -1/3
Row Operation 3: Add 4/3 times the 2nd row to the 1st row
Step 2: Interpret the reduced row echelon form
The reduced row echelon form of the augmented matrix is
which corresponds to the system
We see that the variables can take arbitrary numbers; they are called free variables. Let
,
. All solutions of the system are given by
The system has infinitely many solutions.