Solve the simultaneous equations x^2 + y^2 = 9 and x+ y = 2. Give your answer to 2.d.p
Label your two equations 1 and 2 respectively. Make x the subject of the second equation, so x=2-y. Substitute x=2-y into x^2+y^2=9, to give (2-y)^2+y^2=9. Expand the brackets using FOIL to give 4-4y+y^2+y^2=9. By grouping like terms together get 2y^2-4y-5=0. Because the question asks for the answer in 2.d.p, you know to use the quadratic formula, so substitute into the given formula where a=2, b=-4 and c=-5 (dont forget the minus sign!). Using the + and the - sign you get y=2.87 and y=-0.87. Then substitute these values into x+y=2 to get x=-0.87 and x=2.87.
GS
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