Question

How do you solve
X+y=11
Xy=30

Answer 1

X+y=11
Xy=30

x=11-y

(11-y)y=30
11y-y²=30
11y-y²-30=0
y²-11y+30=0
y²-5y-6y+30=0
y(y-5)-6(y-5)=0
(y-5)(y-6)=0

y-5=0
y=5

y-6=0
y=6

x=11-y
x=11-5=6

x=11-6=5




x=6 y=5

x=5 y=6

Answer 2

Solve the equation:

`x+y =11` ......[1]

xy = 30 .......[2]

we can write equation [2] as;

`x= (30)/(y)`

Substitute the value of x in [1] we have;

`(30)/(y)+y =11`

or

`(30+y^2)/(y) =11`

`y^2+30 = 11y`

or

`y^2-11y+30 = 0`

`y^2-6y-5y+30 = 0`

`y(y-6)-5(y-6)=0`

`(y-5)(y-6)=0`

By zero product property, we have;

y = 5 and y = 6

Substitute these y values in [1] we get

For y =5 we have;

x +5 =11

Subtract both sides by 5 we get;

x = 6

For y = 6 ;

x +6 =11

Subtract 6 from both sides we get;

x = 5

Therefore, the values of x and y satisfy the given equation are:

if x = 6 then y = 5

and

if x =5 then y = 6