 Hello and welcome to the session. In this session we will discuss a question which says that find the solution of the given system of equations and here the equations are given to us as y is equal to 34 minus x square whole upon 3x and y is equal to 8 plus 3x square whole upon 2x. Now let us start with the solution of the given question. Now here we are given the system of equations. Let this be equation number 1 and this be equation number 2. Now whenever we are given a system of equations of the form y is equal to f of x and y is equal to g of x then the solution is given by the equation f of x is equal to g of x. Now here we are given the equations of the form y is equal to f of x and y is equal to g of x. So the solution will be given by the equation f of x is equal to g of x. So here solution of the given equations is given by the equation 34 minus x square whole upon 3x is equal to 8 plus 3x square whole upon 2x. Now let us multiply we get 35 minus x square whole into 2x is equal to 8 plus 3x square whole into 3x. Now we open the brackets and this implies now 34 into 2x is equal to 68x and minus x square into 2x minus 2x cube is equal to 8 into 3x that is 24x plus 3x square into 3x is plus 9x cube this further implies 68x minus 2x cube minus 24x minus 9x cube is equal to 0. Now let us simplify it by combining the like terms and this implies now 68x minus 24x is 44x and minus 2x cube minus 9x cube is minus 11x cube is equal to 0. Now from these two terms taking minus 11x common it will be minus 11x into minus 4 plus x square the whole is equal to 0. All we can write it as minus 11x into x square minus 4 the whole is equal to 0. Now dividing both sides by minus 11 we have x into x square minus 4 the whole is equal to 0. Now this implies x into x square minus now 4 can be written as 2 square the whole is equal to 0. Now using this formula we have x into x minus 2 the whole into x plus 2 the whole is equal to 0. This implies x is equal to 0 2 and minus 2 now when x is equal to 0 then both the given functions will become undefined so x cannot be equal to 0 and we are left with only two values of x that is x is equal to 2 and x is equal to minus 2. So for x is equal to 2 and x is equal to minus 2 we will obtain the corresponding values of y for this we put the value of x either in equation 1 or in equation 2. So let us use equation 1 first of all let us put x is equal to 2 in equation 1 and we have y is equal to 34 minus 2 square whole upon 3 into 2 this implies y is equal to 34 minus 4 whole upon 6 which implies y is equal to 30 upon 6 which is equal to 5. So for x is equal to 2 we get y is equal to 5. Now let us put x is equal to minus 2 in equation 1 for this we get y is equal to 34 minus of minus 2 whole square whole upon 3 into minus 2 which implies y is equal to 34 minus now minus 2 whole square is 4 and upon 3 into minus 2 is minus 6 and this implies y is equal to 30 upon minus 6 which is equal to minus 5. Now for x is equal to minus 2 we get y is equal to minus 5 now here for x is equal to 2 we have obtained y is equal to 5. So here we have the ordered pair 2 5 and for x is equal to minus 2 we have obtained y is equal to minus 5. So here we have the ordered pair minus 2 minus 5. So we get two solutions of the given system of equations that is the ordered pair 2 5 and the ordered pair minus 2 minus 5. Now when we draw the graph of the two curves we see that the two curves intersect at two points that is the point which coordinates 2 5 and the point which coordinates minus 2 minus 5. Now here a red curve is the graph of the function y is equal to 34 minus x square whole upon 3x and blue curve is the graph of the function y is equal to 8 plus 3x square whole upon 2x. Thus the solution of the given system of equations is given by the ordered pairs 2 5 and minus 2 minus 5. Now we can also check that these two ordered pairs form the solution of the given system of equations by putting these ordered pairs in the given equations. Now here you can see we have got two solutions of the given system of equations that is the ordered pair 2 5 and the ordered pair minus 2 minus 5. Now here we have checked that the ordered pair 2 5 forms the solution of the given system of equations by putting x is equal to 2 and y is equal to 5 in both the equations and here you can see this ordered pair satisfies both the equations. This means the ordered pair 2 5 forms the solution of the given system of equations. Similarly the ordered pair minus 2 minus 5 will also satisfy the given two equations. So we have found the solution of the given system of equations and this completes our session. Hope you all have enjoyed the session.