root x + y=11 and x +rooty=7 solve it by elimination method calculate x and y

Sunday, August 24, 2014

You may use substitution method better such
that:

$\displaystyle{y}={11}-\sqrt{}$
x

Plugging $\displaystyle{11}-\sqrt{{x}}$ instead of y in the second
equation yields:

$\displaystyle{x}+\sqrt{{{11}-\sqrt{{x}}}}=$
7

Subtracting x both sides
yields:

$\displaystyle\sqrt{{{11}-\sqrt{{x}}}}={7}-$
x

Raising to square both sides
yields:

$\displaystyle{11}-\sqrt{{x}}={49}-{14}{x}+$
x^2

Subtracting 11 both sides
yields:

$\displaystyle-\sqrt{{x}}=-{14}{x}+{{x}}^{{2}}+{49}-$
11

$\displaystyle\sqrt{{x}}={14}{x}-{{x}}^{{2}}-$
38

$\displaystyle{x}={{\left({14}{x}-{{x}}^{{2}}-{38}\right)}}^{{2}}=\gt{x}={196}{{x}}^{{2}}+{{x}}^{{4}}+{1444}-$
28x^3 - 1064x + 76x^2

$\displaystyle{{x}}^{{4}}-{28}{{x}}^{{3}}+{272}{{x}}^{{2}}-{1065}{x}+$
1444 = 0

The zeroes of this equation are among the
divisors of 1444.

The solutions to the system
of equations is $x = D_{1444}$ and $y = 11 - sqrt (D_{1444})$
.

Help Notes