How to solve y=x^3 and y=x^2 simultaneously?

x³ = x²
x³ - x² = 0
x ² ( x - 1) = 0
x = 0 , x = 1
y = 0 , y = 1

(0,0) , (1,1)

y = x^3 (solve by using substitution)
y = x^2

y = x^3
x^2 = x^3
x^3 - x^2 = 0
x^2(x - 1) = 0

x^2 = 0
x = ±√0
x = 0

x - 1 = 0
x = 1

y = x^2
y = 0^2
y = 0

y = 1^2
y = 1

∴ (x = 0 , y = 0) , (x = 1 , y = 1)

Label y=x^3 as equation 1
y=x^2 as equation 2
Then substitute equation 1 into 2 we get x^3=x^2
Then x^3 - x^2=0
Factorise x^2(x - 1)=0
Then x=0 or 1
Substitute x=0 into equation 1
y= 0^3
y=0

Substitute x=1 into equation 1
y=1^3
y=1

y = x^3
y = x^2
Subtract the two equations to get:
x^3 - x^2 = y - y
x^3 - x^2 = 0
x^2(x - 1) = 0
x = 0 or x = 1
If x = 0, y = 0 (after substituting x in original equation)
If x = 1, y = 1 (after substituting x in original equation)

x³ = x²
x³ - x² = 0
x²(x - 1) = 0
x = 0 or 1

x^3 - x^2 = 0
x^2 (x-1) = 0
x = 0 or 1
y = 0 or 1
the 2 curves intersect in (0,0) & (1,1)

Set equal to each other. Recognize that x =0, 1 are the answers.

It is not possible to solve them simultaneously.

If y = x^3 and y = x^2 are not simultaneous equations since,

x^3 not equal to x^2


-rds