 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that, find the solution of the given system of equations and the equations given are x raised to power 4 minus y is equal to 0 and x square plus y is equal to 2. Now let us start with the solution of the given question. Here we are given the system of equations that is x raised to power 4 minus y is equal to 0. Let us mark this equation as equation number 1 and x square plus y is equal to 2. Let us mark this equation as equation number 2. Now we will use substitution method to solve the system of equations. Now we can rewrite equation number 2 as y is equal to 2 minus x square. Now we put this value of y in equation number 1 and we get x raised to power 4 minus of y that is minus of 2 minus x square the whole is equal to 0 which implies that x raised to power 4 minus of 2 plus x square is equal to 0 and it can also be written as x raised to power 4 plus x square minus 2 is equal to 0. Let x square be equal to z so this polynomial now becomes z square plus z minus 2 and this equation can be written as z square plus z minus 2 is equal to 0. Now this is a quadratic equation in z. We shall solve this quadratic equation using factorization method. So we have z square now plus z can also be written as minus z plus 2z minus 2 is equal to 0. This implies that now taking z common from first two terms we get z into z minus 1 the whole plus again taking two common from last two terms we have 2 into z minus 1 the whole is equal to 0 which further implies that z plus 2 the whole into z minus 1 the whole is equal to 0 which implies z is equal to 1 and minus 2 so we have got two values of z but we need to find values of x we have x square is equal to z for z is equal to 1 we have x square is equal to 1 which implies that x is equal to plus minus of square root of 1 which further implies that x is equal to plus minus of 1. Now for z is equal to minus 2 we have x square is equal to minus 2 but square of a number is never negative so we have only two values of x that is x is equal to 1 which implies 1 and x is equal to minus 1. Now we obtain corresponding values of y for this we put the value of x either in equation 1 or in equation 2. Let us use equation 2 to obtain value of y when x is equal to 1 we have 1 square minus 1 which implies that z is equal to plus y is equal to 2 which implies that 1 square is 1 plus y is equal to 2 which further implies that y is equal to 2 minus 1 which is equal to 1 for x is equal to 1 we have y is equal to 1 so we have the ordered pair 1 1 similarly when x is equal to 1 we have the ordered pair 1 we have minus 1 whole square plus y is equal to 2 which implies that minus 1 whole square is 1 plus y is equal to 2 which further implies that y is equal to 2 minus 1 that is equal to 1 for x is equal to minus 1 y is equal to 1. The second ordered pair is minus 1 1 so we have two solutions of the given system of equations given by the ordered pairs 1 1 and minus 1 1. Now if we see the following figure here this red curve represents the graph of the equation x square plus y is equal to 2 and this blue curve represents the graph of the equation x raised to power 4 minus y is equal to 0. We see that these two curves intersect at two points given by the ordered pairs minus 1 1 and 1 1 thus the solutions of the given system of equations are given by the ordered pairs 1 1 and minus 1 1 which is the required answer. This completes our session hope you enjoyed this session.