To solve the system of equations by inspection, we have:
- \( y = \frac{3}{5}x - 5 \)
- \( y = -\frac{3}{5}x - 5 \)
Let's analyze these equations.
The first equation represents a line with a positive slope (\(\frac{3}{5}\)) and a y-intercept of -5.
The second equation represents a line with a negative slope (\(-\frac{3}{5}\)) and the same y-intercept of -5.
Both lines cross the y-axis at the same point (0, -5), which means they start at the same point vertically. However, they have different slopes, which means they will diverge away from each other.
Since they are two distinct lines that meet at only one point (the y-intercept), they will only intersect at one point.
To find that point, we can set the equations equal to each other:
\[ \frac{3}{5}x - 5 = -\frac{3}{5}x - 5 \]
Solving for \(x\):
\[ \frac{3}{5}x + \frac{3}{5}x = -5 + 5 \] \[ \frac{6}{5}x = 0 \] \[ x = 0 \]
Substituting \(x = 0\) back into either equation to find \(y\):
Using \(y = -\frac{3}{5}(0) - 5\):
\[ y = -5 \]
So, the point of intersection is \((0, -5)\).
Since the two lines are not the same line, but they intersect at a unique point, the answer to the system of equations is:
D. (0, -5)