Solve the given system of linear equations by inspection.

Question

y=35x−5

y=−35x−5

(1 point)
Responses

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

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

no solution
no solution

infinitely many solutions

Answer 1

To solve the system of equations by inspection, we look at the two equations:

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

We can equate the two expressions for \( y \):

\( 35x - 5 = -35x - 5 \)

Now, we can add \( 35x \) to both sides:

\( 35x + 35x - 5 = -5 \)

This simplifies to:

\( 70x - 5 = -5 \)

Next, we add 5 to both sides:

\( 70x = 0 \)

Dividing both sides by 70 gives:

\( x = 0 \)

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

Using the first equation:

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

Thus, we find the solution:

\( (x, y) = (0, -5) \)

This means the solution to the system of equations is:

\( (0, -5) \).