Solve algebraically the following if there is a solution: x+y=3 2x+y=5 x^2+y=6

First we realize that the question asks IF there is a solutionLet us start with the simplest equations, x+y=3 and 2x+y=5By subtracting the first equation from the second we see x=2 and subbing into x+y=3 we get 2+y=3 and so y=1Now does this 'agree' with our third equation? subbing our values in for x and y into x^2+y=9 we get 2^2+1=5 which means 5=5 which is clearly true. So x=2 and y=1 are the solutions to all three equations.