Question

Solve the given system of linear equations by inspection.

y=3/5x−5

y=−3/5x−5

Answers:
(0,-5)
no solution
infinitely many solutions
(-5,0)

Answer 1

To solve the given system of linear equations by inspection, we have:

1. \( y = \frac{3}{5}x - 5 \)
2. \( y = -\frac{3}{5}x - 5 \)

### Step 1: Check if the equations are parallel
The slopes of the two lines can be found directly from the equations:

- For the first equation \( y = \frac{3}{5}x - 5 \), the slope is \( \frac{3}{5} \).
- For the second equation \( y = -\frac{3}{5}x - 5 \), the slope is \( -\frac{3}{5} \).

Since the slopes are different, the lines are not parallel and will intersect at some point.

### Step 2: Find the intersection point
We can set the two equations equal to each other to find the point of intersection:

\[
\frac{3}{5}x - 5 = -\frac{3}{5}x - 5
\]

### Step 3: Solve for \( x \)
Add \( \frac{3}{5}x \) to both sides:

\[
\frac{3}{5}x + \frac{3}{5}x = -5 + 5
\]

This simplifies to:

\[
\frac{6}{5}x = 0
\]

Now divide by \( \frac{6}{5} \):

\[
x = 0
\]

### Step 4: Substitute \( x \) back to find \( y \)
Now we can substitute \( x = 0 \) back into either equation to find \( y \):

Using the first equation:

\[
y = \frac{3}{5}(0) - 5 = -5
\]

### Conclusion
The solution to the system of equations is the point:

\[
(0, -5)
\]

So the answer is \( (0, -5) \).