Question

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.

Responses

Infinitely Many Solutions
Infinitely Many Solutions - incorrect

One Solution
One Solution - no response given

No Solutions

Answer 1

no

Answer 2

it has no solutions

Answer 3

To determine the number of solutions of the system of linear equations, we can first rewrite the equations in the standard form:

1) −x + y = 3
2) −2x + 2y = 3

Let's simplify the second equation by dividing it by 2:

−x + y = 3/2

Now we can see that the two equations are equivalent, which means they represent the same line. Therefore, the system of equations has infinitely many solutions.

Answer 4

I apologize for the mistake in my previous response.

Let's rewrite the equations:

1) -x + y = 3
2) -2x + 2y = 3

We can see that the second equation is a multiple of the first equation. This means that the two equations represent the same line and therefore have infinitely many solutions.

Answer 5

To determine the number of solutions of the system of linear equations, let's rewrite the equations:

1) -x + y = 3
2) -2x + 2y = 3

By comparing the two equations, we can see that they are equivalent. Thus, the system of equations does not have a unique solution. The equations represent parallel lines since they have the same slope but different y-intercepts.

Therefore, the system of equations has no solutions.