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Solving equations help

Solve the equations
x^2 + y^2 = 20
x + y = 6
Make y (or x) the subject of the second equation and substitute into the first.
Question: x^2 y^2=20 Call This Equation 1 x y=6 Call This Equation 2Make xor y the subject in equation 2( I will make x the subject:smile:Therefore, I have x=6-y Call This Equation 3I can now sub in x 6-y into equation 1 (sub 3 into 1)So i get (6-y)^2 y^2=20Now expand the first brackets out (6-y)(6-y) which equals y^2-12y 36So now y^2-12y 36 y^2=20Tidy it up:2y^2 -12y 36=20And i can see a quadratic equation about to be formed with the y^2, so make it equal zeroSo, 2y^2-12y 16=0Now factorise: (2y-8)(y-2)Therefore 2y-8=0 or y-2=0So: y=4 or y=2Now sub in y=4 into equation 2 and find x so x 4=6therefore when y=4, x= 2Now sub in y=2 into equation 2 and find xso x 2=6therefore when y=2, x=2:biggrin:

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