Is my answer correct?
Write the system of equations as an augmented matrix. Then solve for x and y.
−4x−y=6
12x-2y=-8
Solution =
-1,-2
to check, put it back in
-4(-1) -(-2) = ? yes 6
12(-1) -2(-2) = ? yes -8
LOL, forgot the old easy stuff :)
To check if your answer is correct, we need to convert the system of equations into an augmented matrix and solve it using matrix operations.
The system of equations is:
-4x - y = 6 ...(1)
12x - 2y = -8 ...(2)
To convert this into an augmented matrix, we arrange the coefficients of x, y, and the constants into a matrix form:
| -4 -1 | 6 |
| 12 -2 | -8 |
Now, we can perform row operations to solve for x and y. Let's use Gaussian elimination:
1. Multiply the first row by -3 and add it to the second row to eliminate the x term in the second equation:
| -4 -1 | 6 |
| 0 1 | -26 |
2. Divide the second row by 1 to get a leading 1 in the row:
| -4 -1 | 6 |
| 0 1 | -26 |
3. Multiply the second row by 4 and add it to the first row to eliminate the y term in the first equation:
| -4 0 | -110 |
| 0 1 | -26 |
4. Divide the first row by -4 to get a leading 1 in the row:
| 1 0 | 27.5 |
| 0 1 | -26 |
The resulting augmented matrix represents the system of equations:
x = 27.5
y = -26
Your answer of (-1, -2) is not correct. The correct solution is (x, y) = (27.5, -26).