The problem is to find $x$ and $y$. $$\sqrt x + y = 7$$ $$\sqrt y +x = 11$$ I know what the answer is, but I am confused about how to get the answer. Here’s the picture of the problem: https://m.imgur.com/gallery/7Q8asNU
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Graphing the two equations and finding their point of intersection is one of the ways to go; it seems much more troublesome analytically. – Manan Aug 16 '20 at 04:24
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https://math.stackexchange.com/questions/144910/system-of-equations-x2y-7-y2x-11 – lab bhattacharjee Aug 16 '20 at 04:48
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2Does this answer your question? System of equations: $x^2+y=7, y^2+x=11$ – Siong Thye Goh Aug 16 '20 at 05:26
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That is not a solution. @Manan – William Elliot Aug 16 '20 at 05:30
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@WilliamElliot It does reveal one of the solutions, though. – Manan Aug 16 '20 at 08:12
1 Answers
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$$\sqrt{x}=7-y$$
$$\sqrt{y}=11-x$$
Square both sides of each:
$$x=49-14y+y^2$$
$$y=121-22x+x^2$$
Substitute the first equation into the second:
$$y=121 -22(49-14y+y^2) + (49-14y+y^2)^2$$
And you have a quartic in $y$. Be careful with the solutions that you get, though. Squaring both sides can create extra solutions to the equation so you'll need to substitute them back into the your original system to check which ones are valid.
