We are solving the system of linear equations:

1. $3x + y = 7$
2. $x + y = 5$

Step 1: Eliminate $y$

Subtract the second equation from the first to eliminate $y$:

$(3x + y) - (x + y) = 7 - 5$

Simplify:

$2x = 2$

Solve for $x$:

$x = 1$

Step 2: Substitute $x = 1$ into one of the original equations

Substitute $x = 1$ into $x + y = 5$:

$1 + y = 5$

Solve for $y$:

$y = 4$

Solution:

The solution to the system of equations is:

$x = 1, \, y = 4$

Would you like details or have any questions? Here are related questions you might explore:

1. How do you solve a system of linear equations graphically?
2. Can we use substitution for solving this system?
3. How does elimination work in solving systems of equations with more variables?
4. Can systems of linear equations have no solution or infinite solutions?
5. What are the applications of solving systems of equations?

Tip: Always check your solution by substituting the values back into both original equations!