The equations are geometrically shown by a pair of coincident lines. Ifthe solutions of the equations are given by the common points. then what are the common points in this case? Scale xaxis 1 cm-100 units yaxis: 1em=100 units From the graph, we observe that every point on the line is a common solution to both the equations. So, they have infinitely many solutions as both the equations are equivalent. Such pairs of equations are called consistent and dependent pair of linear equations in two variables. This system of equations that has solution are known as "consistent equations
4.2.3 RELATION BETWEEN COEFFICIENTS AND NATURE OF SYSTEM OF EQUATIONS
Leta, b, c, and a, b, c, denote the coefficients of a given pair of linear equations in two variables. Then, let us write and compare the values of in the above examples.
Scale xaxis 1 cm-100 units yaxis: 1em=100 units From the graph, we observe that every point on the line is a common solution to both the equations. So, they have infinitely many solutions as both the equations are equivalent. Such pairs of equations are called consistent and dependent pair of linear equations in two variables. This system of equations that has solution are known as "consistent equations