Question

Determine the number of solutions of this system of linear equations:%0D%0A%0D%0A−x+y=3%0D%0A−%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A3%0D%0A %0D%0A%0D%0A−2x+2y=3%0D%0A−%0D%0A2%0D%0A%0D%0A+%0D%0A2%0D%0A%0D%0A=%0D%0A3%0D%0A %0D%0A%0D%0AThis question requires you to show your work.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0ANo Solutions%0D%0ANo Solutions%0D%0A%0D%0AOne Solution%0D%0AOne Solution%0D%0A%0D%0AInfinitely Many Solutions

Answer 1

To determine the number of solutions of the system of linear equations, we can first write it in matrix form:

```
| -1 1 | | x | | 3 |
| -2 2 | * | y | = | 3 |
```

Then, we can find the determinant of the coefficient matrix:

det = (-1)(2) - (-2)(1) = -2 + 2 = 0

Since the determinant is 0, the system has either no solutions or infinitely many solutions. To determine which one it is, we can proceed with solving the system using row operations:

R2 = R2 + 2R1

```
| -1 1 | | x | | 3 |
| 0 4 | * | y | = | 9 |
```

Now we can easily solve for y:

4y = 9
y = 9/4

Substitute y back into the first equation:

-x + 9/4 = 3
-x = 3 - 9/4
x = 3/4

Therefore, the system has one unique solution, and the solution is x = 3/4, y = 9/4.

So, the final answer is: One Solution