You are given the system of linear equations:

1. \( x + y = 1 \)
2. \( x - y = 3 \)

To solve this system, let's add the two equations:

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

Simplifying both sides:

\[
2x = 4
\]

Now, solve for \( x \):

\[
x = \frac{4}{2} = 2
\]

Next, substitute \( x = 2 \) into one of the original equations, say \( x + y = 1 \):

\[
2 + y = 1
\]

Solve for \( y \):

\[
y = 1 - 2 = -1
\]

Thus, the solution is:

\[
x = 2, \quad y = -1
\]

### Do you want more details or have any questions?

Here are 5 related questions to expand on this:
1. How do we solve systems of equations using substitution?
2. Can we solve this system graphically?
3. What is the determinant of the coefficient matrix for this system?
4. What if the system had more than two variables?
5. How does the elimination method compare to substitution for larger systems?

**Tip:** For solving larger systems of equations, matrix methods like Gaussian elimination or using inverse matrices can be very effective.

Learn how to solve the system of linear equations x + y = 1 and x - y = 3 step-by-step using the substitution method. This problem involves fundamental concepts of algebra and systems of equations, suitable for high school students.

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