Simultenous Equations

**JohnDoe** · March 9th 2009, 09:50 AM

How to solve $x+\sqrt{y}=4$ and $y+\sqrt{x}=3$ Thanks in advance. x=? y=?

**e^(i*pi)** · March 9th 2009, 10:04 AM

Originally Posted by JohnDoe

How to solve $x+\sqrt{y}=4$ and $y+\sqrt{x}=3$ Thanks in advance. x=? y=?

rearranging:

$\sqrt{y} = 4-x$ so $y = (4-x)^2 = 16-8x+x^2$

$\sqrt{x} = 3-y$ so $x = (3-y)^2 = 9-6y+y^2$

Sub in (4-x)^2 for y:

$x = (3-16+8x-x^2)^2$

solve for x and the put the value(s) of x into one of the original equations to find y

**JohnDoe** · March 9th 2009, 10:55 AM

xsoy I did not get the meaning. Can you explain?

Thanks for reply but I can not figure out how to do it can anyone provide me the exact solution. Also I am not experienced with MathType so I had to edit the post a few times the correct one would be $x+\sqrt{y}=4$ and $y+\sqrt{x}=3$ .

There must be a trick in solving this problem because it is an examination question and we are not supposed to use calculators while solving with the method you suggest I think it is impossible to get an accurate solution without a calculator.

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