Question

A system of two linear equations in two variables x and y is rewritten as the following augmented matrix:

[ 6 6 | -18 ]
[ -4 -2 | 2 ]
Use the Gauss-Jordan Elimination Method to solve for x and y.
x = _________
y = _________

Answer 1

x = -10

y = 1

Explanation:

To use the Gauss-Jordan Elimination Method to solve for x and y, we need to put the augmented matrix in row-echelon form. The first step is to eliminate the x-coefficient in the second row by adding 4 times the first row to the second row. This gives us the following matrix:

[ 6 6 | -18 ]

[ 0 -10 | -10 ]

Next, we need to eliminate the y-coefficient in the second row. We can do this by adding 5 times the second row to the first row, which gives us the following matrix:

[ 1 -10 | -10 ]

[ 0 -10 | -10 ]

Now, the matrix is already in row-echelon form, so we can read the solution directly from the matrix. The solution is x = -10 and y = 1. Therefore, the solutions to the system of linear equations are:

x = -10

y = 1

Note that there may be other solutions to the system of equations, depending on the specific equations that the matrix represents. The Gauss-Jordan Elimination Method will always give us one possible solution, but there may be other solutions as well.