solve this using gaussian elimination
x+5y=7
-x-7y=-5
To solve the system of equations using Gaussian elimination, follow these steps:
Step 1: Write the system of equations in matrix form:
```
| 1 5 | | x | | 7 |
| -1 -7 | | y | = | -5 |
```
Step 2: Perform row operations to transform the coefficient matrix into row echelon form.
- Multiply the first equation by -1 and add it to the second equation to eliminate the -1 coefficient on the second equation:
```
| 1 5 | | x | | 7 |
| 0 -2 | | y | = | -2 |
```
Step 3: Divide the second equation by -2 to make the leading coefficient 1:
```
| 1 5 | | x | | 7 |
| 0 1 | | y | = | 1 |
```
Step 4: Perform back substitution to solve for the variables.
- Substitute the value of y = 1 into the second equation:
```
x + 5(1) = 7
x + 5 = 7
x = 7 - 5
x = 2
```
Step 5: The solution is x = 2 and y = 1.
Therefore, the solution to the system of equations is x = 2 and y = 1.