CHAPTER II - LINEAR EQUATIONS IN TWO UNKNOWNS

Abstract

This chapter discusses linear equation in two variables. Elementary algebra deals with equations such as 3x = 5, x − 2y = −8, and −x + 3y − 2z = 14. These are classed as first-degree equations, also called linear equations, because their unknown quantities appear no more than once in each term and only with the understood exponent. An equation like 4xy − 7 is, therefore, not linear because its unknown quantities, x and y, appear in the term 4xy. For many mathematical purposes, it is also important to identify equations according to the number of unknown quantities which they contain. This chapter explores linear equations in two unknowns. A set of equations considered together in connexion with the same problem is called a system of simultaneous equations or, for short, a system of equations. A solution of an equation, or of a system of equations, is a set of values for the unknown quantities that satisfy the mathematical conditions expressed by the equation or equations. When only one such set of values for the unknowns is possible, the solution is said to be a unique solution. When all possible solutions for a system of equations have been found, the system is said to have been solved simultaneously.