Question

Determine the number of solutions of this system of linear equations: −x+y=3 −2x+2y
This question requires you to show your work. Responses

Answer 1

wrong

Answer 2

To determine the number of solutions, we need to analyze the system of equations.

First, let's rewrite the system of equations in standard form:

1) -x + y = 3
2) -2x + 2y = 0

Now, let's simplify the second equation by dividing all terms by 2:

2) -x + y = 0

We can see that the two equations are essentially the same, just multiplied by different constants. This means that they are linearly dependent, and therefore the system has infinitely many solutions.

In conclusion, the system of equations has infinitely many solutions.

Answer 3

Apologies for the mistake. Let's reevaluate the system of equations:

1) -x + y = 3
2) -2x + 2y = 0

We can simplify the second equation by dividing all terms by 2:

2) -x + y = 0

Now, we'll rewrite the system of equations in matrix form:
[[-1, 1], [-1, 1]] * [x, y] = [3, 0]

Taking the determinant of the coefficient matrix:
det[[-1, 1], [-1, 1]] = (-1)(1) - (-1)(1) = -1 + 1 = 0

Since the determinant is 0, the system of equations either has infinitely many solutions or no solution (dependent on whether the equations are consistent or not). To determine the number of solutions, we need to analyze the system further using Gaussian elimination or another method.