x-y=10, x+y=14

To solve the system of equations given:

1. \( x - y = 10 \)
2. \( x + y = 14 \)

We can use the method of substitution or elimination. Here, we'll use elimination.

First, let's add the two equations together:

\[ (x - y) + (x + y) = 10 + 14 \]

This simplifies to:

\[ 2x = 24 \]

Now, divide both sides by 2:

\[ x = 12 \]

Now that we have the value of \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use the second equation:

\[ x + y = 14 \]

Substituting \( x = 12 \):

\[ 12 + y = 14 \]

Now, solve for \( y \):

\[ y = 14 - 12 = 2 \]

So the solution to the system of equations is:

\[ x = 12, \quad y = 2 \]