Pair of Linear Equations in Two Variables — Chapter Summary

An equation of the form ax

An equation of the form ax + by + c = 0, where a, b, c are real numbers and a² + b² ≠ 0. Example: 2x + 3y - 6 = 0. When plotted on a coordinate plane,

Three possibilities exist

Three possibilities exist: (1) Intersecting lines - unique solution (exactly one point of intersection), (2) Parallel lines - no solution (lines never

For equations a₁x + b₁y +

For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0: If a₁/a₂ ≠ b₁/b₂, lines intersect (unique solution). If a₁/a₂ = b₁/b₂ = c₁/c₂, lines coincide

Plot both equations as lines on

Plot both equations as lines on the same coordinate system. Find at least two points for each line by substituting x-values and calculating correspond

Step 1

Step 1: From one equation, express one variable in terms of the other (y = mx + c form). Step 2: Substitute this expression into the second equation t