Write the system of equations as an augmented matrix. Then solve for x and y.
-3x+3y=-21
3x+2y=-4
-3 +3 -21
+3 +2 -4
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1 0 2
0 1 -5
x= 2, y = -5
Please Help. ax + by = c
dx + ey = f
Using the gauss jordan elimination
To write the system of equations as an augmented matrix, we will rearrange the equations and put all coefficients and constants into a single matrix.
The given system of equations is:
-3x + 3y = -21 ...(1)
3x + 2y = -4 ...(2)
To form the augmented matrix, we create a matrix with all the coefficients of the variables and the constants on the right side, separated by vertical bars:
| -3 3 | -21 |
| 3 2 | -4 |
Now, to solve for x and y, we can use row operations on this augmented matrix and reduce it to row-echelon form or reduced row-echelon form. Let's proceed with row-echelon form.
We'll perform row operations to simplify the matrix:
1. Multiply row 1 by 1/(-3): (R1)
|-3/(-3) 3/(-3) | -21/(-3) |
| 3 2 | -4 |
Simplifying row 1:
| 1 -1 | 7 |
| 3 2 | -4 |
2. Multiply row 1 by 3 and subtract from row 2:
| 1 -1 | 7 |
| 0 5 | -25 |
Simplifying row 2:
| 1 -1 | 7 |
| 0 1 | -5 |
3. Add row 2 to row 1:
| 1 0 | 2 |
| 0 1 | -5 |
The matrix is now in row-echelon form. To solve for x and y, we can read the solutions from the matrix.
From row 1: 1x + 0y = 2
x = 2
From row 2: 0x + 1y = -5
y = -5
Therefore, the solution to the system of equations is x = 2 and y = -5.