Determine the number of solutions of this system of linear equations: −x+y=3 −2x+2y=3 This question requires you to show your work. (1 point)

Question

Responses
Infinitely Many Solutions Infinitely Many Solutions
One Solution One Solution
No Solutions No Solutions

show your work.

Answer 1

To determine the number of solutions of this system of linear equations, we can rewrite the system in matrix form and use row reduction:

| -1 1 | 3 |
| -2 2 | 3 |

R2 = R2 + 2R1:

| -1 1 | 3 |
| 0 4 | 6 |

R2 = R2/4:

| -1 1 | 3 |
| 0 1 | 1.5 |

R1 = R1 - R2:

| -1 0 | 1.5 |
| 0 1 | 1.5 |

Now, the matrix is in row-echelon form. The number of solutions depends on whether the system of equations is consistent or not. Since the matrix has a pivot in every column, the system is consistent and has one unique solution.

Therefore, the number of solutions for this system of linear equations is: One Solution.