SOLUTION: Please help me solve this by using the substitution method. Thank you! {{{ x^2+y^2=90 }}} {{{ y=sqrt(x) }}}

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Question 1061541: Please help me solve this by using the substitution method. Thank you!



Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Please help me solve this by using the substitution method. Thank you!


~~~~~~~~~~~~~~~~~~~~~~ 

 = 90,    (1)
y = .         (2)

Square equation (2) (both sides). You will get

 = x.

Using this, replace  by "x" in the equation (2). You will get

 = 90,      (1')   or

 = 0.

Solve by using the quadratic formula. You will get

 =  = .


Thus  = 9,   = -10.


Since "x" under the square root must be non-negative, only the root x= 9 survives.

Then y =  = +/- 3.


Answer. There are 2 solutions: (x,y) = (9,3)  and  (x,y) = (9,-3).


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