To solve the system of equations by inspection, we have the following two equations:
- \( y = 35x - 5 \)
- \( y = -35x - 5 \)
We can set these equations equal to each other because they both equal \( y \):
\[ 35x - 5 = -35x - 5 \]
Next, we'll solve for \( x \) by first adding \( 35x \) to both sides:
\[ 35x + 35x - 5 = -5 \] \[ 70x - 5 = -5 \]
Now, we can add \( 5 \) to both sides:
\[ 70x = 0 \]
Dividing both sides by \( 70 \):
\[ x = 0 \]
Now that we have the value of \( x \), we can find the corresponding value of \( y \) by substituting \( x = 0 \) into either equation. Using the first equation:
\[ y = 35(0) - 5 = -5 \]
Thus, we have the solution \( (0, -5) \).
Now, checking if this point satisfies both equations:
For the first equation:
\[ y = 35(0) - 5 = -5 \]
For the second equation:
\[ y = -35(0) - 5 = -5 \]
Both equations are satisfied by the point \( (0, -5) \).
The solution to the system of equations is:
\[ (0, -5) \]
Thus, the correct response is:
(0,−5)