To solve the system of equations using the elimination method, follow these steps:
1. Write down the system of equations:
[tex]\[
\begin{array}{l}
a - b = 8 \\
a + b = 20
\end{array}
\][/tex]
2. Add the two equations together to eliminate [tex]\( b \)[/tex]:
[tex]\[
(a - b) + (a + b) = 8 + 20
\][/tex]
Simplifying this, we get:
[tex]\[
2a = 28
\][/tex]
3. Solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{28}{2}
\][/tex]
[tex]\[
a = 14
\][/tex]
4. Substitute [tex]\( a = 14 \)[/tex] back into one of the original equations to solve for [tex]\( b \)[/tex]:
We can use the first equation:
[tex]\[
14 - b = 8
\][/tex]
Subtract 14 from both sides:
[tex]\[
-b = 8 - 14
\][/tex]
Simplifying this, we get:
[tex]\[
-b = -6
\][/tex]
Multiply both sides by -1:
[tex]\[
b = 6
\][/tex]
5. Thus, the solution to the system of equations is:
[tex]\[
(a, b) = (14, 6)
\][/tex]
6. Final answer:
The correct ordered pair from the given options is:
[tex]\[
(14, 6)
\][/tex]
