To determine the value of [tex]\( x \)[/tex] in the given system of equations:
[tex]\[
\begin{cases}
x + 3y = 2 \\
4x - 3y = 23
\end{cases}
\][/tex]
we will use the method of elimination. Here is the step-by-step solution:
1. First, we will add the two equations to eliminate [tex]\( y \)[/tex].
[tex]\[
(x + 3y) + (4x - 3y) = 2 + 23
\][/tex]
2. Combine like terms:
[tex]\[
x + 4x + 3y - 3y = 2 + 23
\][/tex]
This simplifies to:
[tex]\[
5x = 25
\][/tex]
3. Solve for [tex]\( x \)[/tex] by dividing both sides by 5:
[tex]\[
x = \frac{25}{5}
\][/tex]
[tex]\[
x = 5
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\( 5 \)[/tex]. The correct answer is (B) 5.
