Question

Solve the given system of linear equations by inspection.

y=35x−5

y=−35x−5

(1 point)
Responses

infinitely many solutions
infinitely many solutions

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

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

no solution

Answer 1

To solve the system of equations by inspection, let's analyze the given equations:

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

These two equations represent two straight lines.

The first equation \( y = 35x - 5 \) has a positive slope of 35, which means it rises steeply as \( x \) increases. The second equation \( y = -35x - 5 \) has a negative slope of -35, meaning it falls steeply as \( x \) increases.

To find the points of intersection, set the right-hand sides of both equations equal to each other:

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

Now, simplify this equation:

1. Add \( 35x \) to both sides:
\[
35x + 35x - 5 = -5
\]

2. Combine like terms:
\[
70x - 5 = -5
\]

3. Add 5 to both sides:
\[
70x = 0
\]

4. Divide both sides by 70:
\[
x = 0
\]

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

Using the first equation:
\[
y = 35(0) - 5 = -5
\]

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

Since the two lines have different slopes, they will intersect at this single point. Therefore, the solution to the system is:

\[
\text{(0, -5)}
\]

Thus, the correct response is:

**(0, −5)**