Verified Answer :

Julik

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:

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




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