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)
Responses
Infinitely Many Solutions Infinitely Many Solutions
One Solution One Solution
No Solutions No Solutions
show your work.
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.