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 parenthesisno solutionno solutioninfinitely many solutions

Answer 1

To solve the system of equations by inspection, let's first write the given equations clearly:

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

Now, we can set these two equations equal to each other since they both equal \( y \):

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

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

\[
35x + 35x - 5 = -5
\]
\[
70x - 5 = -5
\]

Now, add 5 to both sides:

\[
70x = 0
\]

Dividing by 70 gives us:

\[
x = 0
\]

Now, we can substitute \( x = 0 \) back into either of the original equations to find \( y \). Let's substitute it into the first equation:

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

Thus, we have found one solution to the system:

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

To confirm, we can plug \( x = 0 \) into the second equation:

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

Both equations give us the same value for \( y \), confirming that our solution is correct.

Thus, the solution to the system of equations is:

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