Question

Why linear equation in two variable has infinite solutions

Answer 1

Consider the equation ax+by=c.

Now we know that there is a number d=lcm(a,b).

Let ad1=d and bd2=d. So, ad1−bd2=0. Note that neither d1 nor d2is 0.

ax+by+ad1−bd2=ca(x+d1)+b(y−d2)=c

Thus, for every solution of this linear diophantine equation of two variables, there exists another unique solution. Hence, there is an infinite number of solutions to this equation.


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Answer 2

Linear equation is an equation which has highest degree as one with two variables


For example

x+y=2

This equation can be drawn on a graph as a line. As line has infinite points and each point is a solution of it. Therefore, linear equation in two variables have infinite solutions