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

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You may use substitution method better such that:

`y = 11 - sqrt x`

Plugging `11 - sqrt x` instead of y in the second equation yields:

`x + sqrt(11 - sqrtx) = 7`

Subtracting x both sides yields:

`sqrt(11 - sqrtx) = 7 - x`

Raising to square both sides yields:

`11 - sqrtx = 49 - 14x + x^2`

Subtracting 11 both sides yields:

`-sqrt x = -14x + x^2 + 49 - 11`

`` `sqrt x = 14x - x^2 - 38`

`x = (14x - x^2 - 38)^2 =gt x = 196x^2 + x^4 + 1444 - 28x^3 - 1064x + 76x^2`

`` `x^4 - 28x^3 + 272x^2 - 1065x + 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})` .**