Certainly! Let's solve the given system of equations using the elimination method.
The system of equations is:
[tex]\[
\begin{array}{l}
12x - y = 25 \\
9x + y = 17
\end{array}
\][/tex]
### Step 1: Add the Equations to Eliminate [tex]\( y \)[/tex]
First, we'll add the two equations together to eliminate [tex]\( y \)[/tex].
[tex]\[
(12x - y) + (9x + y) = 25 + 17
\][/tex]
When we add the two equations, the [tex]\( y \)[/tex] terms will cancel each other out:
[tex]\[
12x - y + 9x + y = 42
\][/tex]
Simplifying this:
[tex]\[
21x = 42
\][/tex]
### Step 2: Solve for [tex]\( x \)[/tex]
Next, we'll solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 21:
[tex]\[
x = \frac{42}{21}
\][/tex]
[tex]\[
x = 2
\][/tex]
### Step 3: Substitute [tex]\( x \)[/tex] Back into One of the Original Equations
Now, we'll substitute [tex]\( x = 2 \)[/tex] back into one of the original equations to solve for [tex]\( y \)[/tex]. Let's use the second equation [tex]\( 9x + y = 17 \)[/tex]:
[tex]\[
9(2) + y = 17
\][/tex]
Solving for [tex]\( y \)[/tex]:
[tex]\[
18 + y = 17
\][/tex]
[tex]\[
y = 17 - 18
\][/tex]
[tex]\[
y = -1
\][/tex]
### Conclusion
The solution to the system of equations is the ordered pair [tex]\( (2, -1) \)[/tex].
So, the correct answer is:
A. [tex]\( (2, -1) \)[/tex]
