Question

Use the elimination method to solve the system of equations. Choose the correct ordered pair.
x+y=8
x-y= 6
Solution: choose your answer...

Answer 1

To solve the system of equations using the elimination method, we start with the following equations:

1) \( x + y = 8 \)
2) \( x - y = 6 \)

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 \((7, 1)\).