Pair of Linear Equations in Two Variables

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. For example: 2x + 3y - 6 = 0. When graphed, this represents a

Step

Step-by-step approach: 1) Convert each equation to y = mx + c form, 2) Plot both lines on same graph, 3) Find intersection point. Example: For x + y =

Algebraic method

Algebraic method: 1) Solve one equation for one variable, 2) Substitute this expression into the other equation, 3) Solve for the remaining variable,

Algebraic method

Algebraic method: 1) Make coefficients of one variable equal by multiplication, 2) Add or subtract equations to eliminate that variable, 3) Solve for

A pair that has at least

A pair that has at least one solution. When a₁/a₂ ≠ b₁/b₂, the lines intersect at exactly one point (unique solution). Example: x + y = 5 and 2x - y =