To solve the system of equations:
- \( x + y = 6 \)
- \( x - y = 4 \)
We can solve this system using the method of substitution or elimination. Here, I will use elimination:
First, we can add the two equations to eliminate \( y \):
\[ (x + y) + (x - y) = 6 + 4 \]
This simplifies to:
\[ 2x = 10 \]
Now, divide both sides by 2:
\[ x = 5 \]
Now that we have \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use the first equation:
\[ 5 + y = 6 \]
Subtract 5 from both sides:
\[ y = 1 \]
So the solution to the system of equations is:
\( x = 5 \) and \( y = 1 \).
The solution is \( (5, 1) \).