Question

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

Answer 1

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)**