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
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.
no
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.
it has no solutions
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.