 Hello and welcome to the session. In this session, we will discuss how a linear equation in one variable can have one solution, no solution or infinitely many solutions. Now, by solution, we mean that value of the variable from which the left hand side of the equation and the right hand side of the equation are equal. Now, linear equation in one variable x can be of the type Ax plus B is equal to D or Ax plus B is equal to Cx plus D. So, for solution we see those values of variable x for which left hand side is equal to right hand side of the equation. Now, let us see linear equation in one variable with only one solution or we can say linear equation in one variable with unique solution. Now, consider the equation 3 y plus 7 is equal to 16. Now, let us solve this equation. So, this implies 3 y is equal to 16 minus 7 and further this implies 3 y is equal to 16 minus 7 is 9 and this implies y is equal to 9 upon 3 which is equal to 3. Now, let this be equation number 1. Now, here the only value of y that makes the equation number 1 true is y is equal to 3. It means for y is equal to 3 left hand side will be equal to right hand side of this equation. Now, let us verify this for this. We will put y is equal to 3 in equation 1 and here we will get 3 into 3 plus 7 is equal to 16 which implies 9 plus 7 is equal to 16 and further this implies 16 is equal to so left hand side is equal to right hand side it means y is equal to 3 satisfies equation 1. Now, if we put any other value of variable y then left hand side will not be equal to right hand side of this equation. Now, let us put y is equal to 1 in equation 1. Now, here we have 3 into 1 plus 7 is equal to 16 which implies 3 plus 7 is equal to 16 and this means 10 is equal to 16 which is not true because 10 is not equal to 16. So, putting y is equal to 1 in equation 1 left hand side is not equal to right hand side. Similarly, if we put any other value of variable y except 3 then it will not satisfy equation 1. So, the given equation has only one solution that is y is equal to 3. So, this is the linear equation in one variable with only one solution. Now, let us discuss linear equation in one variable with infinitely many solutions. Now, here consider the equation 4 x plus 20 is equal to 4 into x plus 5 the whole. Now, here left hand side is equal to 4 x plus 20 and right hand side is equal to 4 into x plus 5 the whole which is equal to 4 into x plus 4 into 5 which is 20. So, right hand side is also equal to 4 x plus 20. So, these two expressions are equivalent. Now, simplifying the given equation we get 4 x plus 20 is equal to, now here using the distributive property this will be 4 into x that is 4 x plus 4 into 5 that is 20. Now, subtracting 4 x from both sides we get 20 is equal to 20 which is true. So, 4 x plus 20 is equal to 4 into x plus 5 the whole is true for all real values whatever may be the value of x the two expressions remain equivalent. The given equation many solutions. Hence, if we put any value of x then will be equal to right hand side of this equation. Now, let us verify this for this let us put x is equal to 3 and 5 in this equation. Now, for x is equal to 3 left hand side will be equal to 4 x plus 20 which is equal to into 3 plus 20 which is equal to 12 plus 20 and this is equal to 30 and right hand side which is equal to 4 into x plus 5 the whole will be equal to 4 into 3 plus 5 the whole and this is equal to 4 into 3 plus 5 is 8 and 4 into 8 is 32. So, 32 is equal to 32 which means left hand side is equal to right hand side. So, x is equal to 3 as the solution of the given equation. Now, for x is equal to 5 left hand side which is equal to 4 x plus 20 will be equal to 4 into 5 plus 20 and this is equal to 20 plus 20 which is equal to 40 right hand side which is equal to 4 into x plus 5 the whole will be equal to 4 into 5 plus 5 the whole and this is equal to 4 into 5 plus 5 which is 10 and 4 into 10 is 40. T is equal to which means left hand side is equal to right hand side. So, x is equal to 5 is the solution of the given equation. We can put any real value of x in this equation and that will be the solution of this equation. This is a linear equation in one variable with infinite many solutions and now let us discuss linear equation in one variable with no solution. Now, where an equation has no solution equation. Now, when every value of x left hand side is not equal to right hand side then the equation is inconsistent that is it has no solution. Now, this condition ends when two expressions are not equivalent. Now, let us consider an equation that is 5x minus 2 is equal to 5 into x plus 1 the whole here. First of all, let us simplify this equation. Now, this implies 5x minus 2 is equal to now using the distributed property this is equal to 5x plus 5 into 1 which is 5 now subtracting 5x from both sides we get minus 2 is equal to 5 which is not minus 2 is not equal to 5. So, here left hand side is not equal to right hand side it means these two expressions are not equivalent. Therefore, the given equation is not true any real value. So, the given equation has no solution. This is the linear equation in one variable with no solution. So, in this session we have learnt about linear equation in one variable with one solution no solution or if I write you many solutions and this completes our session hope you all have enjoyed this session.