Problem

8. Determine if the statement below is true or false.
The point $(-4,9)$ is the solution to the system below.
\[
\begin{array}{c}
-x+y=5 \\
2 x-y=-17
\end{array}
\]
False
True

Answer

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Answer

Final Answer: The statement "The point $(-4,9)$ is the solution to the system below" is \(\boxed{False}\).

Steps

Step 1 :Substitute the given point into the system of equations and check if both equations are satisfied.

Step 2 :For the first equation, substituting $(-4,9)$ gives $4+9=13$, which is not equal to $5$. So, the first equation is not satisfied.

Step 3 :For the second equation, substituting $(-4,9)$ gives $-8-9=-17$, which is equal to $-17$. So, the second equation is satisfied.

Step 4 :Since the first equation is not satisfied by the point $(-4,9)$, the point is not a solution to the system of equations.

Step 5 :Final Answer: The statement "The point $(-4,9)$ is the solution to the system below" is \(\boxed{False}\).

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