Understand systems of equations through their graphs: intersection points, parallel lines, and coincident lines.
The solution to a system of two linear equations is the point where the two lines cross on a graph. To find it graphically: 1. Graph both lines 2. Find the intersection point 3. Read the coordinates (x, y) With Desmos on the SAT, this is incredibly fast: - Type both equations - Click on the intersection point - Read the answer This method is sometimes faster than algebra, especially for messy …
| Graph appearance | Number of solutions | Algebraic result | |---|---|---| | Lines cross at one point | One solution | You find (x, y) | | Lines are parallel (same slope, different intercept) | No solution | You get 0 = 5 (false) | | Lines overlap completely (same line) | Infinitely many | You get 0 = 0 (true) |
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