x^2 + 2y^2 =17 5x-3y=9 solve x and y
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hala718
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x^2 + 2y^2 =17.....(1)
5x-3y =9.....(2)
We are going to use the substitution method to solve the system
5x-3y = 9
==> x= (3y+9)/5
Now substitute x in (1)
X^2 + 2Y^2 = 17
[(3y+9)/5]^2 +2y^2 = 17
(9y^2 + 54y + 81)/25 + 2y^2 =17
(59/25)y^2 + (54/25)y+ 81/25 =17
(59/25)y^2 + 54/25)y -344/25 =0
Multiply by 25
==> 59y^2 +54y -344=0
==> (y-2)(59y+172)
==> y1= 2 ==> x1= (3y+9)/5 = 15/5 =3
and y2= -172/59 ==> x2= 0.051 (approx.)
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