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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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.

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