Question 10 - of 25 Step 1 of 1 Determine if the point $$ (-2,-5) $$ is the point of intersection for the given lines. In other words, is $$ (-2,-5) $$ the solution to the system of equations? $$ \begin{array}{r}-2 x+3 y=-19 \ 5 x-3 y=-5\end{array} $$ Answer 2 Points Nomit O The point $$ (-2,-5) $$ satisfies neither equation. It is not the point of intersection of the two lines. $$ (-2,-5) $$ satisfies one of the equations, but not both. It is not the point of intersection of the two lines. The point $$ (-2,-5) $$ satisfies both equations, so it is the solution to the system and the point of intersection of the two lines.

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UpStudy AI · Accepted Answer

To determine whether the point $$ (-2, -5) $$ is the point of intersection for the given system of equations:

$$
\begin{cases}
-2x + 3y = -19 \
5x - 3y = -5
\end{cases}
$$

**Step 1: Substitute $$ x = -2 $$ and $$ y = -5 $$ into each equation.**

1. **First Equation:**
   $$
   -2(-2) + 3(-5) = 4 - 15 = -11
   $$
   The left side equals $$-11$$, which does **not** equal $$-19$$.

2. **Second Equation:**
   $$
   5(-2) - 3(-5) = -10 + 15 = 5
   $$
   The left side equals $$5$$, which does **not** equal $$-5$$.

**Conclusion:**

Since the point $$ (-2, -5) $$ does **not** satisfy either of the two equations, it is **not** the solution to the system. Therefore, $$ (-2, -5) $$ is **not** the point of intersection of the two lines.

**Correct Answer:**
- **The point $$ (-2,-5) $$ satisfies neither equation. It is not the point of intersection of the two lines.**
The point $$ (-2, -5) $$ does not satisfy either equation, so it is not the point of intersection of the two lines.

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