Question

X+y=27
Xy=180
find x and y​

Answer 1

Answer:

x+y=27 ..(equation 1)

xy=180 ..(equation 2)

xy=180

y=180/x. ....

now put the value of y in equation 1

=x+y=27

=x+180/x=27

=

$\frac{ {x}^{2} + 180 }{x} = 27$

=x²+180= 27x

= x²-27x+180=0

=x²-(15+12)x+180=0

=x²-15x-12x+180=0

=x(x-15)-12(x-15)=0

=(x-15)(x-12)=0

x=15; x=12

now put the value of x in equation 1

=x+y=27

=15+y=27

=y=27-15

=y=12

or

=x+y=27

=12+y=27

=y=27-12

=y=15

Hope it will help you..

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thank you..

Answer 2

Step-by-step explanation:

$Given, \\ x + y = 27 \\ xy = 180 \\ \\ x + y = 27 \\ x = 27 - y \\ \\ xy = 180 \\ (27 - y)y = 180 \\ 27y - {y}^{2} = 180 \\ {y}^{2} - 27y + 180 = 0 \\ \\ {y}^{2} - 27y + 180 = 0 \\ {y}^{2} - 15y - 12y + 180 = 0 \\ y(y - 15) - 12(y - 15) = 0 \\ (y - 15)(y - 12) = 0 \\ y - 15 = 0 \: \: or \: \: y - 12 = 0 \\ y = \underline{ \underline{ 15}} \: \: or \: \: y = \underline{ \underline{12}} \\ \\ If \: \: y = 12, \: \: x = 15 \\ If \: \: y = 15, \: \: x = 12 \\ \\ 15 + 12 = 27 \\ 15 \times 12 = 180$