Is \( (-7,3) \) a solution to this system of equations? \[ \begin{array}{l} 2 x-3 y=-23 \\ x-6 y=-20 \end{array} \] yes

First, let's plug in \( x = -7 \) and \( y = 3 \) into the first equation: \( 2(-7) - 3(3) = -14 - 9 = -23 \). This checks out! Now, for the second equation: \( -7 - 6(3) = -7 - 18 = -25 \), which does NOT equal -20. So, while the first equation holds, the second does not. Hence, \( (-7, 3) \) is NOT a solution to the system of equations. Now, isn't it fascinating to think about how systems of equations have helped us in real life? They are often used in fields like economics to determine equilibrium points, or in engineering to model forces acting on structures. Solving them can show us how different variables interact! If you're interested in more hands-on experience, try graphing the lines represented by both equations. The point of intersection (if one exists) gives you the solution! Not only does this method provide a visual understanding, but it’s also quite satisfying to see it all come together on paper.