A good many problems in the natural and social sciences as well as in engineering and the physical sciences deal with eqquations ralating twp sets of variables. An equation of the type ax=b,expressing the variable b in terms of the cariable x and used here because the graph of the equation above is asthaight line.similarly,the equation a1x1+a2x2+...+AnXn=b, expressing b in terms of the variables X1,X2,...Xn and the known constants a1,a2,...,An,is called alinear equation.In many applications we are given b and the constants a1,a2,...An and must find numbers x1,x2,...,Xn, called unknowns, satisfying (1).
A solution to alinear equation (1) is acequence of n numbers s1,s2,...,Sn,which has the property that (1) is satisfied when x1=s1,x2=s2,...Xn=Sn are subsituted in (1).