Solve the simultaneous equations x + y = 1 , x^2 -2xy+y^2=9

So here we want to eliminate one variable so we are only working with either x or y by themself, so to do this we can rearrange the first equation of x+y=1 to x= 1-y. This new equation can therefore be substituted into the second equation to replace all the ‘x’ values. This will create the equation (1-y)^2 -2(1-y)y + y^2 =9. We then expand this expression to get 1-4y+4y^2=9, which can be rearranged to 4y^2-4y-8 = 0. The common factor 4 can be taken out, and we can factorise this expressions into 4(y-2)(y+1)=0. We can calculate that the values of y are y=2 and y=-1. Using the first equation, when y=2, this means that x=-1; and when y=-1, x=2.