Solve the system of equations by first writing it in matrix form and then using Gauss-Jordan elimination.
x-4y =-5
-2x + 9y = 125
I don't know if I am using the same form or "Gauss-Jordan" elimination.
2x - 8y = -10
-2x + 9y = 125
Add the two equations.
y = 115
Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.
Thank you greatly!
To solve the system of equations using Gauss-Jordan elimination, we first need to write the system of equations in matrix form.
Let's represent the system of equations as:
| 1 -4 | | x | = | -5 |
| -2 9 | | y | | 125 |
Here, the left side of the equation represents the coefficient matrix, the middle represents the variables, and the right side represents the constants.
To solve the system using Gauss-Jordan elimination, we can follow these steps:
Step 1: Set up the augmented matrix.
We can write the augmented matrix by combining the coefficient matrix and the constants on the right side.
| 1 -4 -5 |
| -2 9 125 |
Step 2: Perform row operations to transform the matrix into row-echelon form.
Start with the topmost left element (1 in the first row and first column) and use row operations to eliminate the other elements in the first column.
R2 = R2 + 2R1
| 1 -4 -5 |
| 0 1 115 |
Now, we have transformed the matrix into row-echelon form.
Step 3: Continue performing row operations to obtain the reduced row-echelon form.
Divide the second row by its leading coefficient to get a leading entry of 1.
R2 = R2/1
| 1 -4 -5 |
| 0 1 115 |
Next, eliminate the element in the first row and second column.
R1 = R1 + 4R2
| 1 0 -5 |
| 0 1 115 |
Now, we have obtained the reduced row-echelon form.
Step 4: Interpret the resulting matrix.
The reduced row-echelon form tells us that x = -5 and y = 115.
Therefore, the solution to the system of equations is x = -5 and y = 115.