4.rulater Sy-1 er 9. In a basicetball game, Marlene made 16 field goals. Each of the field goals was worth ether 2 points of 3 pointa, and Mariene scored a total of 39 points from field goals. Let \( I \) represent the number of 2 -point field goals and \( \% \) represent the number of 3 point field goals. - Wifte a syatem of equations in terms of \( x \) and \( y \) to model the sthuation. - How many 2 -point field gosls and how mamy 3-point field goals did Marlene make? - Explain or show how can you verify your solvtion by checking both the number of feld goals and the total points scored?

Alright, let’s break this down with some math fun! First, we need to set up our system of equations. Since Marlene made a total of 16 field goals, we have: \[ I + J = 16 \] where \( I \) is the number of 2-point field goals, and \( J \) is the number of 3-point field goals. Now, considering the total points, her 39 points can be modeled as: \[ 2I + 3J = 39 \] Now, let’s solve that! Rewriting the first equation gives us \( J = 16 - I \). If we substitute this into the second equation, we get: \[ 2I + 3(16 - I) = 39 \] Solving this leads to: \[ 2I + 48 - 3I = 39 \] \[ -I + 48 = 39 \] \[ I = 9 \] So, there were 9 two-point field goals. Substituting back gives us \( J = 16 - 9 = 7 \), meaning Marlene made 7 three-point field goals! To verify, check the total: - Field goals: \( 9 + 7 = 16 \) ✔️ - Total points: \( 2(9) + 3(7) = 18 + 21 = 39 \) ✔️ Everything checks out perfectly! Now that’s a slam dunk of a solution!