Given the system of equations 4x-y=-5 2(x-1)=3(y+1) verify if x^3>y^3?

To verify if the cube of x is larger than the cube of y,
we need to determine the values of x and y, therefore, we'll have to solve the
system.

We'll use substitution method. We'll re-write the
first equation, isolating y to the left side:

-y = -4x -
5

y = 4x + 5

We'll re-write
the 2nd equation in terms of x:

2(x-1) = 3(4x + 5 +
1)

We'll remove the
brackets:

2x - 2 = 12x +
18

We'll isolate the terms in x to the left
side:

2x - 12x = 18 + 2

-10x =
20

x = -2

We'll determine
y:

y = 4*(-2) + 5

y = -8 +
5

y = -3

We'll raise to cube
the values of x and y:

`x^3 =
(-2)^3`

`x^3 = -8`

`y^3 =
(-3)^3`

`y^3 =
-27`

We notice that -8 > -27,
therefore the inequality `x^3 > y^3` is
verified.