#AP SAT (Digital) Prep: Linear Systems and Inequalities 🚀

Hey there! Let's get you prepped for the AP SAT (Digital) exam with a super-focused review of linear systems and inequalities. Think of this as your ultimate cheat sheet for acing those questions! We're going to break it all down, make it stick, and get you feeling confident. Let's do this! 💪

#Linear Systems: Where Lines Meet (or Don't!)

#Solutions of Linear Systems, Graphically

Think of linear systems as a group of lines hanging out on a graph. The solutions are all about where these lines interact. It's like a party, and we're looking for where the guests (lines) mingle!

#Intersection Points and Solutions

• System of Linear Equations: Two or more linear equations sharing the same variables. It's like having multiple rules that need to be followed at the same time.
• Solution: The point(s) where the graphs of the equations intersect. These points satisfy all equations simultaneously. Think of it as the place where all the rules are happy.
• Intersection Point (x, y): This point makes all the equations true at the same time. It's the magical spot that satisfies everyone.
• Parallel Lines: No solution! They never meet, so there's no common point that satisfies both equations. It's like two people walking in the same direction, but never meeting.
• Coincident (Overlapping) Lines: Infinitely many solutions! These lines are the same, so every point on the line is a solution. It's like two identical twins - they're always together.

#Types of Solutions

• One Unique Solution: Lines intersect at one point. This is the most common scenario. 🎯
• No Solution: Parallel lines with the same slope but different y-intercepts. They're going in the same direction but will never meet. 🚫
• Infinitely Many Solutions: Coincident lines with the same slope and y-intercept. They are the same line, so every point is a solution. ♾️
• Systems with Three or More Equations: Can have no solution, one unique solution, or infinitely many solutions, depending on the relationships between the lines. It ...