Question

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

Answer 1

Answer:

Solve the equation:

$x+y =11$            ......[1]

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

we can write equation [2] as;

$x= \frac{30}{y}$

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

$\frac{30}{y}+y =11$

or

$\frac{30+y^2}{y} =11$

$y^2+30 = 11y$

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

Answer 2

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