Question

solve x+y=19 and x²+y²=185 ​

Answer 1

Step-by-step explanation:

when x=11, y=8

x=8 ,y=11

Answer 2

$x + y = 19 \: \: \: \: \: - (1)$

${x}^{2} + {y}^{2} = 185 \: \: \: \: - (2)$

$x = 19 - y \: \: \: - (3)$

Substituting equation 3 in 2 ,

${(19 - y)}^{2} + {y}^{2} = 185$

$361 - 38y + {y}^{2} + {y}^{2} = 185$

$2 {y}^{2} - 38y = - 176$

$2 {y}^{2} - 38y + 176 = 0$

Using Quadratic formula ,

$\bf \: x = \dfrac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a}$

$= \dfrac{38± \sqrt{1444 - 1408} }{4}$

$= \dfrac{38±6}{4}$

$\therefore \: \bf \: x = 11 \: and \: 8$

Substituting x values in equation 1 , We get ,

$\bf \: y = 8 \: and \: 11$

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