 Hello and welcome to the session. In this session we will discuss a question which says that solve the following system of equations by substitution method and the system of equations is given as 3x-5y is equal to minus 1, 2x-y is equal to minus 3. Now let us start with the solution of the given question. Here we are given the system of linear equations and we have to solve it by using substitution method. Now let this be equation number 1 and this be equation number 2. First of all we will express y in terms of x by using. Can you have the two given equations? So here let us express y in terms of x by using equation number 2 and from equation number 2 we get 2x-y is equal to minus 3 which implies now subtracting 2x from both sides we have minus y is equal to minus 3 minus 2x and this implies now multiplying both sides of the equation by minus 1 we have y is equal to 3 plus 2x or we can write it as y is equal to 2x plus 3. Now let this be equation number 3. Now we will substitute this value of y in the other equation that is in equation number 1. So substituting y is equal to 2x plus 3 in equation 1 we get 3x minus 5y that is minus 5 into 2x plus 3 the whole is equal to minus 1 and this implies 3x and here minus 5 into 2x will be minus 10x and minus 5 into 3 will be minus 15 is equal to minus 1 which implies now 3x minus 10x will be minus 7x minus 15 is equal to minus 1. This further implies now we will add 15 on both sides and we get minus 7x is equal to minus 1 plus 15 and this implies minus 7x is equal to 14. Now dividing both sides by minus 7 we get x is equal to 14 upon minus 7 which implies x is equal to minus 2. Now this is equation number 3. Now to obtain the value of y we will put x is equal to minus 2 in equation number 3 and we get y is equal to 2 into minus 2 plus 3 which implies y is equal to minus 4 plus 3 and this gives y is equal to minus 1. So we get x is equal to minus 2 and y is equal to minus 1. Hence x is equal to minus 2 and y is equal to minus 1 is the solution of the given equations. Now let us verify it. Now we can check whether x is equal to minus 2 and y is equal to minus 1 is the solution of the given equations by putting these values in the given equations. First of all let us put x is equal to minus 2 and y is equal to minus 1 in equation 1 and this is equation number 1. So here we have 3 into minus 2 minus 5 into minus 1 is equal to minus 1 and this implies now 3 into minus 2 is minus 6 and minus 5 into minus 1 is plus 5 is equal to minus 1 which implies minus 1 is equal to minus 1 which is true. Similarly we will put x is equal to minus 2 and y is equal to minus 1 in equation number 2. So here we have 2 into minus 2 minus of minus 1 is equal to minus 3 which implies now 2 into minus 2 is minus 4 minus of minus 1 is plus 1 is equal to minus 3 and this implies now minus 4 plus 1 is minus 3 is equal to minus 3 which is again true. So x is equal to minus 2 and y is equal to minus 1 satisfies both the equations. Hence x is equal to minus 2 and y is equal to minus 1 is the solution of the given equations. And this is the solution of the given question. That's all for this session. Hope you all have enjoyed this session.