Use Gauss-Jordan to solve
3x + 2y = -4
4x – 2y = -10
Why do it the hard way?
Add the two equations to get
7x = -14
x = -2
y = (-4 -3x)/2 = 1
To apply the Gauss-Jordan method, read this:
http://mathrefresher.blogspot.com/2007/04/gauss-jordan-elimination.html
It seems like a waste of time to me.
3x+4y=38
5x-5y=-30
To solve the system of equations using the Gauss-Jordan elimination method, follow these steps:
Step 1: Write the augmented matrix for the given system of equations.
The augmented matrix is formed by combining the coefficients and constants of the system of equations. For the given system:
3x + 2y = -4
4x – 2y = -10
The augmented matrix can be written as:
[ 3 2 | -4 ]
[ 4 -2 | -10 ]
Step 2: Perform row operations to transform the matrix into row-echelon form.
Start by focusing on the first column. We can eliminate the 4 in the (2,1) position by performing the following row operation:
-4R1 + 3R2 → R2
The resulting augmented matrix after row operations is:
[ 3 2 | -4 ]
[ 0 -10 | -22 ]
Step 3: Continue performing row operations to transform the matrix into reduced row-echelon form.
To make the coefficient in the (2,2) position equal to 1, divide the second row by -10:
R2 / -10 → R2
The resulting augmented matrix is:
[ 3 2 | -4 ]
[ 0 1 | 2.2 ]
Next, eliminate the 2 in the (1,2) position by performing the following row operation:
-2R2 + 3R1 → R1
The resulting augmented matrix is:
[ 3 0 | -8.8 ]
[ 0 1 | 2.2 ]
Step 4: Continue performing row operations to obtain the solution.
To make the coefficient in the (1,1) position equal to 1, divide the first row by 3:
R1 / 3 → R1
The resulting augmented matrix is:
[ 1 0 | -2.93 ]
[ 0 1 | 2.2 ]
The solution to the system of equations is x = -2.93 and y = 2.2.