To solve the system of equations using the elimination method, we start with the following equations:
- \( x + y = 8 \)
- \( x - y = 6 \)
We can eliminate \( y \) by adding the two equations together:
\[ (x + y) + (x - y) = 8 + 6 \]
This simplifies to:
\[ 2x = 14 \]
Now, divide by 2 to solve for \( x \):
\[ x = 7 \]
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 first equation:
\[ 7 + y = 8 \]
Subtract 7 from both sides:
\[ y = 1 \]
Thus, the solution to the system of equations, in ordered pair form, is:
\((x, y) = (7, 1)\)
So the correct ordered pair is \((7, 1)\).
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