Write a system of equations below as a matrix.
2x-7y=4
X-3y=3
Show all possible steps.
(2 -7) = (4)
(1 -3) = (3)
To represent the system of equations as a matrix, we can write it in the form AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
The given equations are:
2x - 7y = 4 ...... (Equation 1)
x - 3y = 3 ...... (Equation 2)
To represent this system as a matrix, we set up the following:
A = | 2 -7 |
| 1 -3 |
X = | x |
| y |
B = | 4 |
| 3 |
Therefore, the matrix representation of the system of equations is:
| 2 -7 | | x | = | 4 |
| 1 -3 | | y | | 3 |
To represent the given system of equations as a matrix, we need to organize the coefficients of the variables (x and y) and the constant terms (4 and 3).
The variables (x and y) will be represented by the columns of the matrix, and the equations will each be represented by a row. The constant term in each equation will be placed in the last column of the matrix.
Using this method, the matrix representing the system of equations becomes:
```
| 2 -7 | | x | = | 4 |
| 1 -3 | | y | | 3 |
```
So, the matrix representation of the given system of equations is:
```
| 2 -7 |
| 1 -3 |
```
```
| x |
| y |
```
```
=
```
```
| 4 |
| 3 |
```
Remember, the left side of the equation represents the coefficients of the variables (x and y) and the right side represents the constant terms (4 and 3).