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.

To determine if \( (-2,-5) \) is the point of intersection, we need to substitute \( x = -2 \) and \( y = -5 \) into both equations. For the first equation: \(-2(-2) + 3(-5) = 4 - 15 = -11\), which does not equal \(-19\). For the second equation: \(5(-2) - 3(-5) = -10 + 15 = 5\), which does not equal \(-5\). Thus, \( (-2,-5) \) satisfies neither equation! Stay sharp while solving equations! It's crucial to check both equations when determining if a point is a solution. A common mistake is to check only one equation and assume correctness, but each equation must hold true for a point to be an intersection. Don't skip that second check; it could save you embarrassment on tests!