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

Algebra ->  Systems-of-equations -> SOLUTION: Please help me solve this by using the substitution method. Thank you! {{{ x^2+y^2=90 }}} {{{ y=sqrt(x) }}}       Log On


   

Question 1061541: Please help me solve this by using the substitution method. Thank you!
+x%5E2%2By%5E2=90+
+y=sqrt%28x%29+
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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Please help me solve this by using the substitution method. Thank you!
+x%5E2%2By%5E2=90+
+y=sqrt%28x%29+
~~~~~~~~~~~~~~~~~~~~~~ 

x%5E2+%2B+y%5E2 = 90,    (1)
y = sqrt%28x%29.         (2)

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

y%5E2 = x.

Using this, replace y%5E2 by "x" in the equation (2). You will get

x%5E2+%2B+x = 90,      (1')   or

x%5E2+%2B+x+-+90 = 0.

Solve by using the quadratic formula. You will get

x%5B1%2C2%5D = %28-1+%2B-+sqrt+%281+%2B+4%2A90%29%29%2F2 = %28-1+%2B-+19%29%2F2.


Thus x%5B1%5D = 9,  x%5B2%5D = -10.


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

Then y = sqrt%28x%29 = +/- 3.


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