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Solve the given system of linear equations by inspection.

y=35x−5

y=−35x−5

(1 point)
Responses

(0,−5)
left parenthesis 0 comma negative 5 right parenthesis

(−5,0)
left parenthesis negative 5 comma 0 right parenthesis

infinitely many solutions
infinitely many solutions

no solution
no solution

1 answer

To solve the given system of linear equations by inspection, we have:

  1. \( y = 35x - 5 \)
  2. \( y = -35x - 5 \)

Let's set the two equations equal to each other to see if they intersect:

\[ 35x - 5 = -35x - 5 \]

Now, move all terms involving \( x \) to one side:

\[ 35x + 35x = -5 + 5 \]

This simplifies to:

\[ 70x = 0 \]

Dividing both sides by 70 gives:

\[ x = 0 \]

Now, substitute \( x = 0 \) back into either of the original equations to find \( y \):

Using the first equation:

\[ y = 35(0) - 5 = -5 \]

So, the point of intersection is \( (0, -5) \).

Next, let's check the second equation to see if this point also satisfies it:

Using the second equation:

\[ y = -35(0) - 5 = -5 \]

The point \( (0, -5) \) lies on both lines.

Thus, the solution to the given system of equations is:

\[ (0, -5) \]

Therefore, the correct response is:

(0, −5)