<PRE><B>Question 920783</B>


if you&#39;re supposed to solve these 2 equations simultaneously, you would do the following.


x^2 + y^2 = 9 is the first equation


y = 2x is the second equation.


since y = 2x in the second equation, replace y with 2x in the first equation to get:


x^2 + (2x)^2 = 9


simplify to get:


x^2 + 4x^2 = 9


combine like terms to get:


5x^2 = 9


divide both sides of the equation by 5 to get:


x^2 = 9/5


take the square root of both sides of the equation to get:


x = 3/sqrt(5)


replace x with 3/sqrt(5) in the second equation to get:


y = 2x becomes y = 2 * 3 / sqrt(5) = 6 / sqrt(5)


replace x with 3 / sqrt(5) and y with 6 / sqrt(5) in the first equation to get:


x^2 + y^2 = 9 becomes (3/sqrt(5))^2 + (6/sqrt(5))^2 = 9


simplify to get 9/5 + 36/5 = 9


simplify further to get 45/5 = 9


simplify further to get 9 = 9


this confirms the solutions are good.


the solutions are:


x = 3 / sqrt(5) and y = 6 / sqrt(5)


you can simplify these further by rationalizing the denominator to get:


y = 3 * sqrt(5) / 5 and y = 6 * sqrt(5) / 5


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