Question

If x+y=12 and xy=32,then find X and y
answer with explaination
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Answer 1

x = 4, y = 8 or x = 8, y = 4

Explanation:

Given the 2 equations

x + y = 12 → (1)

xy = 32 → (2)

From 2

y =
`(32)/(x)`

Substitute y =
`(32)/(x)` into (1)

x +
`(32)/(x)` = 12 ( multiply through by x )

x² + 32 = 12x ( subtract 12x from both sides )

x² - 12x + 32 = 0 ← in standard form

(x - 4)(x - 8) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x - 8 = 0 ⇒ x = 8

Substitute these values into (1) for corresponding values of y

x = 4 : 4 + y = 12 ⇒ y = 8

x = 8 : 8 + 4 = 12 ⇒ y = 4

Answer 2

Explanation:

x+y=12-----1

xt=32-----2

from 1,

x=12-y-----3

sub 3 into 2

(12-y) y=32

12y-y²=32

y²-12y+32=0

(y-8)(y-4)=0"factorise"

y=8,y=4

sub y =8 into 1,

x+8=12

x=4

sub y =4 into 1

x+4=12

x=8

conclusion,

when x=4,then y=8

when x=8,theb y =4