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
To determine the number of solutions of the system of linear equations, we can look at the coefficients of the variables in the two equations.
The first equation is −x+y=3, which can be rewritten as y = x + 3.
The second equation is −2x+2y=3, which can be rewritten as y = x + 1.
Comparing the two equations, we see that they represent the same line, since they have the same slope (1) and different y-intercepts (3 and 1). Since the two equations are not independent of each other, they represent the same line and therefore have infinitely many solutions.
Therefore, the correct answer is: Infinitely Many Solutions.