Determine the number of solutions of this system of linear equations:

Question

−x+y=3

−2x+2y=3

This question requires you to show your work.

(1 point)
Responses

Infinitely Many Solutions
Infinitely Many Solutions

No Solutions
No Solutions

One Solution

Answer 1

To determine the number of solutions, we need to put the system of equations in matrix form and find its reduced row echelon form.

The system of equations can be represented as:

[-1 1 | 3]
[-2 2 | 3]

Adding 2 times the first row to the second row:

[-1 1 | 3]
[0 4 | 9]

Dividing the second row by 4:

[-1 1 | 3]
[0 1 | 9/4]

Adding the first row to the second row:

[1 0 | -3/4]
[0 1 | 9/4]

From the reduced row echelon form, we see that there is only one solution to this system of equations.