Question

A coordinate grid with 2 lines. The first line passes through (0, negative 5) and (negative 5, 0). The second line passes through (0, negative 5) and (negative 2, 1).
What is the solution to the system of equations?

(5, 0)
(0, 5)
(0, –5)
(–5, 0)

Answer 1

To find the solution to the system of equations defined by the two lines, we'll first determine the equations of each line.

### Line 1
The first line passes through the points (0, -5) and (-5, 0).

To find the slope \( m \):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-5)}{-5 - 0} = \frac{5}{-5} = -1
\]

Using the point-slope form \( y - y_1 = m(x - x_1) \) with the point (0, -5):
\[
y - (-5) = -1(x - 0) \implies y + 5 = -x \implies y = -x - 5
\]

### Line 2
The second line passes through (0, -5) and (-2, 1).

Finding the slope \( m \):
\[
m = \frac{1 - (-5)}{-2 - 0} = \frac{6}{-2} = -3
\]

Using the point-slope form with the point (0, -5):
\[
y - (-5) = -3(x - 0) \implies y + 5 = -3x \implies y = -3x - 5
\]

### Setting the equations equal to find the intersection
Now we have the equations of the two lines:
1. \( y = -x - 5 \)
2. \( y = -3x - 5 \)

Setting them equal to each other:
\[
-x - 5 = -3x - 5
\]

Simplifying this:
\[
-x = -3x
\]
\[
2x = 0 \implies x = 0
\]

Substituting \( x = 0 \) back into one of the line equations to find \( y \):
Using \( y = -x - 5 \):
\[
y = -0 - 5 = -5
\]

Thus, the solution to the system of equations is the intersection point \( (0, -5) \).

### Conclusion
The answer is:
\[
\mathbf{(0, -5)}
\]