Solve for x & y

[nycmathguy]

Solve this system of equations.

x + xy + y = 11
(x^2)(y) + x(y^2) = 30

 

[MathLover1]

x + xy + y = 11............eq.1
(x^2)(y) + x(y^2) = 30..........eq.2

xy + y = 11-x.............1)
(x +1) y = 11-x
y = (11-x)/(x +1)..........substitute in

(x^2)(y) + x(y^2) = 30.............eq.2

(x^2)((11-x)/(x +1)) + x((11-x)/(x +1))^2 = 30

(x (11 - x) (x^2 + 11))/(x + 1)^2 = 30

x (11 - x) (x^2 + 11)= 30(x + 1)^2

x (11 - x) (x^2 + 11)= 30(x + 1)^2

-x^4 + 11 x^3 - 11 x^2 + 121 x=30 x^2 + 60 x + 30

-x^4 + 11 x^3 - 41 x^2 + 61 x - 30 = 0..........using calculator

we get x=1, x=2, x=3, x=5

then

y = (11-x)/(x +1)=(11-1)/(1 +1)=10/2=5
y = (11-x)/(x +1)=(11-2)/(2 +1)=9/3=3
y = (11-x)/(x +1)=(11-3)/(3 +1)=8/4=2
y = (11-x)/(x +1)=(11-5)/(5 +1)=6/6=1

solutions:
x=1, y=5
x=2, y=3
x=3, y=2
x=5, y=1

 

[nycmathguy]

x + xy + y = 11............eq.1
(x^2)(y) + x(y^2) = 30..........eq.2

xy + y = 11-x.............1)
(x +1) y = 11-x
y = (11-x)/(x +1)..........substitute in

(x^2)(y) + x(y^2) = 30.............eq.2

(x^2)((11-x)/(x +1)) + x((11-x)/(x +1))^2 = 30

(x (11 - x) (x^2 + 11))/(x + 1)^2 = 30

x (11 - x) (x^2 + 11)= 30(x + 1)^2

x (11 - x) (x^2 + 11)= 30(x + 1)^2

-x^4 + 11 x^3 - 11 x^2 + 121 x=30 x^2 + 60 x + 30

-x^4 + 11 x^3 - 41 x^2 + 61 x - 30 = 0..........using calculator

we get x=1, x=2, x=3, x=5

then

y = (11-x)/(x +1)=(11-1)/(1 +1)=10/2=5
y = (11-x)/(x +1)=(11-2)/(2 +1)=9/3=3
y = (11-x)/(x +1)=(11-3)/(3 +1)=8/4=2
y = (11-x)/(x +1)=(11-5)/(5 +1)=6/6=1

solutions:
x=1, y=5
x=2, y=3
x=3, y=2
x=5, y=1

Thank you very much. No more monster questions. We will go back to our College Algebra textbook when time allows and when the heatwave goes away. I am moving to my new place on August 7.