What is the value of x in the equation: x + y = 10 and x - y = 2?

To find the value of x in the system of equations provided, we can use the method of elimination or substitution. Here, we will use elimination.

We start with the two equations:

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

To eliminate y, we can add these two equations together:

[ (x + y) + (x - y) = 10 + 2 ]

This simplifies to:

[ 2x = 12 ]

Next, we solve for x by dividing both sides by 2:

[ x = 6 ]

This confirms that the solution for x is 6.

To further validate this solution, we can substitute x back into one of the original equations. Let's use the first one:

[ 6 + y = 10 ]

Solving for y gives:

[ y = 10 - 6 = 4 ]

Now we substitute x and y back into the second equation to ensure both equations hold true:

[ 6 - 4 = 2 ]

Since both conditions are satisfied, our solution ( x = 6 ) is confirmed correct. Thus, the value