can someone please help me solve this question?
I tried so many times but I still could not get it...
2x + 3y = 4
5x + 6y = 16
Augmented Matrix
the ans is supposed to be (8,-4)
thanks in advance
much appreciated
1 3/2 2
1 6/5 16/5
1 3/2 2
0 3/10 -6/5
1 3/2 2
0 3 -12
1 3/2 2
0 1 -4 <<< THERE IS Y
1 3/2 2
0 3/2 -6
1 0 8 <<< THERE IS X
0 1 -4
thanx a million bro!
Sure! I can help you solve this system of equations using the augmented matrix method.
To start, let's represent the given system of equations as an augmented matrix:
| 2 3 | 4 |
| 5 6 | 16 |
Step 1: Perform row operations to get a leading 1 in the first column, first row.
Let's divide the first row by 2:
| 1 3/2 | 2 |
| 5 6 | 16 |
Step 2: Use row operations to obtain zeros below the leading 1.
To eliminate the 5 in the second row, let's multiply the first row by -5 and add it to the second row:
| 1 3/2 | 2 |
| 0 -3/2 | 6 |
Step 3: Simplify the matrix by multiplying the second row by -2/3 to make the coefficient next to the leading 1 equal to 1.
| 1 3/2 | 2 |
| 0 1 | -4 |
Step 4: Now, focus on the second row to get a zero above the leading 1.
Let's multiply the second row by -3/2 and add it to the first row:
| 1 0 | 8 |
| 0 1 | -4 |
The resulting augmented matrix now represents the system of equations in row-echelon form.
Step 5: Convert the augmented matrix back into equations.
From the augmented matrix, we can determine the values of x and y. The first row represents the equation:
- x + 0y = 8, which simplifies to -x = 8, or x = -8.
The second row represents the equation:
0x + y = -4, which simplifies to y = -4.
So, the solution to the system of equations is x = -8 and y = -4. Therefore, the answer is (x, y) = (-8, -4).
I hope this explanation helps you understand how to solve the given system of equations using augmented matrices. Let me know if you have any further questions!