Solve the simultaneous equations: y=x+1, x^2+y^2=13

We already have an expression for y, so we can substitute this in:x²+(x+1)²=x²+(x+1)(x+1) = x²+x²+2x+1=2x²+2x+1 and hence 2x²+2x+1=13 and so 2x²+2x-12=0Now look for common factors. Here we can take out a factor of 2 to get2(x²+x-6)=0And we can use method to factorise to 2(x-2)(x+3) = 0So setting expressions to 0 we have x=2 or x=-3.Substitute values back into expression for y to obtainy = x+1 = 2+1 = 3 or y = -3+1 = -2