To find the number of solutions for the system of linear equations, we can use the method of substitution or elimination. Here, we will use the method of substitution.

The system of equations is:

1) -x + 5y = -1
2) x - y = 2
3) x + 3y = 3

First, let's solve the second equation for x:

x = y + 2

Now, substitute x in the first and third equations:

1) -(y + 2) + 5y = -1
3) (y + 2) + 3y = 3

Solving these equations gives:

1) -y - 2 + 5y = -1
3) 4y + 2 = 3

Solving for y in both equations gives:

1) 4y = 1
3) 4y = 1

So, y = 1/4.

Substitute y = 1/4 into the second equation to find x:

x = 1/4 + 2 = 2.25

So, the solution to the system of equations is x = 2.25, y = 1/4. Since we found a unique solution, the system of equations has one solution.

Question

To find the number of solutions for the system of linear equations, we can use the method of substitution or elimination. Here, we will use the method of substitution.

The system of equations is:

1) -x + 5y = -1
2) x - y = 2
3) x + 3y = 3

First, let's solve the second equation for x:

x = y + 2

Now, substitute x in the first and third equations:

1) -(y + 2) + 5y = -1
3) (y + 2) + 3y = 3

Solving these equations gives:

1) -y - 2 + 5y = -1
3) 4y + 2 = 3

Solving for y in both equations gives:

1) 4y = 1
3) 4y = 1

So, y = 1/4.

Substitute y = 1/4 into the second equation to find x:

x = 1/4 + 2 = 2.25

So, the solution to the system of equations is x = 2.25, y = 1/4. Since we found a unique solution, the system of equations has one solution.

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