Solve the equations x^2+y^2=13 and x-2y=1 simultaneously.

Rearranging the second equation gives x=2y+1. Substituting this into equation 1 gives (2y+1)²+y²=13.Rearrangingthis and factorising the quadratic equation gives (5y-6)(y+2)=0, givingsolutions of y=6/5 and y=-2.Thecorresponding x values are found by substituting these values into equation 2giving: x=17/5 and x=-3 respectively.