SYSTEMS
Finding the precise coordinates where multiple linear equations equate to the same truth. When geometries collide.
01 // The Objective
Where Paths Cross
A system of equations asks: "Is there a pair of (x, y) that works for BOTH lines?" Graphically, this is the exact coordinate where the two lines cross. Drag the sliders in the lab below to map the intersections!
System Visualizer
Line Alpha
y = 1x + 2Line Beta
y = -1x + 402 // Solving Methods
Plot both lines. Look for the intersection. It's the most intuitive method, but can be highly inaccurate if the lines cross at a decimal or fraction.
Solve one equation for a variable, then plug it into the other to collapse the system into a single equation.
Add or subtract entire equations vertically to instantly delete a variable.
03 // Anomalies
Parallel Lines
Same Slope, Different Intercept. They never meet.
Coinciding Lines
Same Slope, Same Intercept. They are the exact same line.
Systems Mastered
You can find the intersection of any paths.