SOLUTION: I've tried solving these equations, and I got (sqrt of 2, 2 sqrt of 2) and (i sqrt of 2, 2i sqrt of 2) {{{ x^2 + y^2 = 9 }}} y = 2x Any way, I'm not sure if I did this right. By

Question 920783: I've tried solving these equations, and I got (sqrt of 2, 2 sqrt of 2) and (i sqrt of 2, 2i sqrt of 2)

y = 2x
Any way, I'm not sure if I did this right. By the way, the "i" in my solution is an imaginary number (sqrt of -1)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

if you'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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