To determine the system of equations that can be graphed to find the solution(s) to the given equation [tex]\(2-9x = \frac{x}{2} - 1\)[/tex], we need to express the equation in terms of two separate equations that can be graphed as lines on a coordinate system.
Let's rewrite the given equation [tex]\(2-9x = \frac{x}{2} - 1\)[/tex]:
1. First, we can rewrite the equation by setting it equal to a common variable, [tex]\(y\)[/tex].
To do that, let's express each side of the equation as a separate equation involving [tex]\(y\)[/tex]:
[tex]\[
\begin{cases}
y = 2 - 9x \\
y = \frac{x}{2} - 1
\end{cases}
\][/tex]
2. Let's analyze this approach in detail:
- The first equation is [tex]\(y = 2 - 9x\)[/tex].
- The second equation is [tex]\(y = \frac{x}{2} - 1\)[/tex].
Since we want to find the system of equations that can be graphed to find the solution(s) to [tex]\(2 - 9x = \frac{x}{2} - 1\)[/tex], we simply take the two equations derived above and set them as our system of equations:
[tex]\[
\left\{
\begin{array}{l}
y = 2 - 9x \\
y = \frac{x}{2} - 1
\end{array}
\right.
\][/tex]
This system of equations can be graphed because both equations are linear, and the intersection point(s) of these lines will give us the solution(s) to the original equation.
Therefore, the correct system of equations is:
[tex]\[
\left\{
\begin{array}{l}
y = 2 - 9x \\
y = \frac{x}{2} - 1
\end{array}
\right.
\][/tex]
