Solve the simultaneous equation x+y=11(1), x^2+y^2=61 (2)

Make x the subject in the equation x+y=11(1). This will help us eliminate x in the second equation (2).x=11-y (3)Substitute (3) into (2)(11-y)²+y²=61Expanding the brackets and simplifying gives 2y²-22y+60=0Dividing the whole equation by 2 gives y²-11y+30=0 (4)(4) is a quadratic equationFactorise, giving (y-5)(y-6)=0There are therefore two solutions, y=5 or y=6Looking back at equation (1), when y=5, x=6when y=6, x=5
Therefore the two solutions are:x=6 y=5x=5 y=6