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 at least one of a or b is not zero (a² + b² ≠ 0). Examples include 3x + 2y

A pair of values (x

A pair of values (x, y) that satisfies both equations simultaneously. For example, if x = 20 and y = 10 satisfy both 3x + 2y = 80 and 4x + 3y = 110, t

Plotting both equations as straight lines

Plotting both equations as straight lines on a coordinate plane. The intersection point gives the solution. Lines can intersect (unique solution), be

Solving one equation for one variable

Solving one equation for one variable in terms of the other, then substituting this expression into the second equation. Steps: express y in terms of

Making coefficients of one variable equal

Making coefficients of one variable equal by multiplying equations by suitable numbers, then adding or subtracting to eliminate that variable. Solve f