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
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