91Ó°ÊÓ

A linear equation in two variables is an equation of the form \(ax + by = c\), where \(a\), \(b\), and \(c\) are constants, and \(x\) and \(y\) are the variables.

A linear equation in two variables can be represented graphically as a straight line plotted on a Cartesian coordinate plane.

A solution of a linear equation is an ordered pair of values for the variables, \((x,y)\), that satisfies the equation. For a given equation, if we substitute the values of the ordered pair for the variables in the equation and the equation holds true, then the ordered pair is a solution of the equation.

A linear equation in two variables can have: 1. Infinite solutions: If two linear equations represent the same line, they have infinitely many common points or solutions (i.e., they are coincident lines). 2. No solution: If two linear equations represent parallel lines, they have no common point or solution (i.e., they are parallel lines). 3. One unique solution: If two linear equations represent intersecting lines, they have one unique common point or solution (i.e., they are intersecting lines). It is crucial to notice that in this problem we are only asked about solutions for "every linear equation in two variables" and not about systems of linear equations in two variables. Therefore, every single linear equation in two variables will have:

Every linear equation in two variables has infinitely many solutions. The solutions can be found by choosing any value for one of the variables and then solving for the other variable to determine its corresponding value.