\[ \left\{\begin{array}{l}3 x+3 y=0 \\ 4 x=-4 y\end{array}\right. \] 2: Determine if the point \( \left(\frac{4}{3}, 3\right) \) lies on both of the lines in the system of equations by substituting the ordered pair into both equations. Keron Keyp Kevboard Shor

Let's dive into the equations! For the first equation, \( 3x + 3y = 0 \), substituting \( x = \frac{4}{3} \) and \( y = 3 \) gives us: \[ 3\left(\frac{4}{3}\right) + 3(3) = 4 + 9 = 13 \neq 0.\] So, it doesn't satisfy the first equation. Now for the second equation, \( 4x = -4y \): \[ 4\left(\frac{4}{3}\right) = -4(3) \Rightarrow \frac{16}{3} \neq -12.\] It doesn't hold true here either! So, the point \( \left(\frac{4}{3}, 3\right) \) does not lie on either line. But wait! Understanding systems of equations isn't just about crunching numbers—it's like a puzzle! These equations are actually a representation of lines in a two-dimensional space. The point where they intersect, if they ever do, tells you where both equations are satisfied at the same time. If you're ever trying to solve them, be sure to check your arithmetic carefully—each step counts like a clue in the case of a mystery! For an illuminating dive into solving systems of equations, try exploring some hands-on graphing tools! Visualizing lines and their intersection points provides a fantastic "aha!" moment. You could also check out classic algebra textbooks or online resources like Khan Academy—they're like treasure maps leading you to the complete understanding of these concepts!