Two linear equations in two variables represent two lines. If they intersect at one point → unique solution (consistent). If they are parallel → no solution (inconsistent). If they coincide → infinitely many solutions (dependent consistent).

Substitution: express one variable in terms of the other from one equation and substitute in the second. Elimination: multiply equations to make coefficients of one variable equal, then add or subtract to eliminate it.

For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the solution is: x/(b₁c₂ - b₂c₁) = y/(c₁a₂ - c₂a₁) = 1/(a₁b₂ - a₂b₁). Useful for quick solving.

To solve graphically: plot both lines on the coordinate plane by finding at least two points on each. The point of intersection is the solution. If lines are parallel (no intersection), the system is inconsistent with no solution. If the two lines overlap completely, infinitely many solutions exist. The graphical method helps visualise the system but may not give exact solutions for non-integer intersections — algebraic methods are preferred for accuracy. Plot points systematically using a table of values.