Lisa and Katie are playing a card game, and a total of 900 points has been scored. Lisa scored 150 more points than Katie. If you let \( l= \) the number of points that Lisa scored, and \( k= \) the number of points that Katie scored, then the problem can be represented by the system: \( l+k=900 \) and \( l=k+150 \) Graph the system. How many points did each of them score? Katie \( =525 \) and Lisa \( =375 \) Katie \( =150 \) and Lisa \( =750 \) Katie \( =375 \) and Lisa \( =525 \) Katie \( =325 \) and Lisa \( =575 \)

To solve this system of equations, first substitute \( l \) from the second equation into the first equation. Since \( l = k + 150 \), you can rewrite the first equation as: \[ (k + 150) + k = 900 \] This simplifies to: \[ 2k + 150 = 900 \] \[ 2k = 750 \] \[ k = 375 \] Now, substitute back to find \( l \): \[ l = k + 150 = 375 + 150 = 525 \] Thus, Katie scored 375 points and Lisa scored 525 points. Now, about the fun stuff: Did you know that card games have a rich historical background? They originated in China around the 9th century AD and evolved across various cultures, leading to the diverse games we have today, from poker to bridge! Each game has its own set of strategies, so next time you play, remember you’re tapping into centuries of gaming evolution! For a real-world application, playing card games can boost critical thinking and enhance social skills. It's more than just fun; card games foster strategic thinking, improve decision-making skills, and are a great way to strengthen friendships. So gather some friends and enjoy a game night; you’re not just playing, you’re also honing your brain!