` 2x + 5y = 1`,
` 2x + 3y = 3`.

Answer

To solve the system of linear equations given by:

1. \( 2x + 5y = 1 \) (Equation 1)
2. \( 2x + 3y = 3 \) (Equation 2)

we will use the elimination method.

### Step 1: Align the equations
We write the equations clearly:

\[ \begin{align*} (1) & \quad 2x + 5y = 1 \\ (2) & \quad 2x + 3y = 3 \end{align*} \]

### Step 2: Eliminate \( x \)
To eliminate \( x \), we can subtract Equation 2 from Equation 1.

\[ (2x + 5y) - (2x + 3y) = 1 - 3 \]

This simplifies to:

\[ 5y - 3y = -2 \]

Which gives us:

\[ 2y = -2 \]

### Step 3: Solve for \( y \)
Now we solve for \( y \):

\[ y = \frac{-2}{2} = -1 \]

### Step 4: Substitute \( y \) back into one of the original equations
We can substitute \( y = -1 \) back into Equation 2 to find \( x \):

\[ 2x + 3(-1) = 3 \]

This simplifies to:

\[ 2x - 3 = 3 \]

### Step 5: Solve for \( x \)
Now we solve for \( x \):

\[ 2x = 3 + 3 \]
\[ 2x = 6 \]
\[ x = \frac{6}{2} = 3 \]

### Step 6: Final solution
Thus, the solution to the system of equations is:

\[ x = 3, \quad y = -1 \]

### Summary of the solution:
The values of \( x \) and \( y \) are:

\[ (x, y) = (3, -1) \]