How many solution does the following system of linear equation have - x + 5y = -1       x - y = 2 x + 3y = 3

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
2. (y + 2) + 3y = 3

Solving these equations gives:

1. -y - 2 + 5y = -1
2. y + 2 + 3y = 3

Simplify to:

1. 4y - 2 = -1
2. 4y + 2 = 3

Solving for y in both equations gives:

1. 4y = 1, so y = 1/4
2. 4y = 1, so y = 1/4

Since y is the same in both equations, the system of equations has a single solution.

To find the value of x, substitute y = 1/4 into the second equation:

x = 1/4 + 2 = 2.25

So, the solution to the system of equations is x = 2.25, y = 1/4.