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On your own paper, solve the system of equations using elimination and identify the solution. Always list your answers alphabetically in the ordered pairs.

[tex]\[
\begin{array}{l}
a - b = 8 \\
a + b = 20
\end{array}
\][/tex]

A. (8, 12)
B. (6, 14)
C. (12, 8)
D. (14, 6)
E. No Solution
F. Infinitely Many Solutions


Sagot :

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]