Question

One Solution, No Solution, or Many Solutions Quick Check
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Question
Solve the given system of linear equations by inspection.

y=35x−5

y=−35x−5

(1 point)
Responses

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

no solution
no solution

infinitely many solutions
infinitely many solutions

(0,−5)
left parenthesis 0 comma negative 5 right parenthesis
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Answer 1

To solve the system of linear equations by inspection:

1. The equations given are:
- \( y = 35x - 5 \)
- \( y = -35x - 5 \)

To find if there are any intersections, we can set both equations equal to each other:

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

2. Adding \( 35x \) to both sides gives us:

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

\[
70x = 0
\]

3. Dividing both sides by 70:

\[
x = 0
\]

4. Now, substitute \( x = 0 \) back into either of the original equations to find the corresponding \( y \)-value. We can use the first equation:

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

5. Thus, the solution to the system of equations is \( (0, -5) \).

The options provided are:
- (−5,0)
- no solution
- infinitely many solutions
- (0,−5)

The correct response is **(0,−5)**.