Question

find x,y values by solving the following equations x³-x+y and y³+x-y​

Answer 1

Answer:

Solve for x

x-y=3

x=3+y

Now plug x into the second equation and solve for y.

x^3-y^3=9

(3+y)^3-y^3 =y

y^3+9y^2+27y+27-y^3=9

9y^2+27y+27=9

y^2+3y+3=1

y^2+3y+2=0

(y+1)(y+2)=0

y=-1; -2

Solve for x using these values and the x equation:

x=3+y

x= 3+(-1), x=3+(-2)

x=2, 1

Now, finally, plus the corresponding x and y values into x+y:

x+y

2+(-1), 1+(-2)

1, -1

So x+y has two possible values: 1 and -1.