which linear system has been correctly solved for one of the variables from the following system? 2x - y = -1 2x y = -7 2x - y =
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Answer:
The system has infinitely many solutions
Step-by-step explanation:
Gauss–Jordan elimination is a method of solving a linear system of equations. This is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.
An Augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.
There are three elementary matrix row operations:
- Switch any two rows
- Multiply a row by a nonzero constant
- Add one row to another
To solve the following system
Step 1: Transform the augmented matrix to the reduced row echelon form
This matrix can be transformed by a sequence of elementary row operations
Row Operation 1: add 1 times the 1st row to the 2nd row
Row Operation 2: add -2 times the 1st row to the 3rd row
Row Operation 3: multiply the 2nd row by -1
Row Operation 4: add -9 times the 2nd row to the 3rd row
Row Operation 5: add 3 times the 2nd row to the 1st row
to the matrix
The reduced row echelon form of the augmented matrix is
which corresponds to the system
The system has infinitely many solutions.