Question

(iv) (2x - 3y) and (3x - 2y)​

Answer 1

Answer:

x = {1.5y, -0.6666666667y}

Step-by-step explanation:

Simplifying

(2x + -3y)(3x + 2y) = 0

Multiply (2x + -3y) * (3x + 2y)

(2x * (3x + 2y) + -3y * (3x + 2y)) = 0

((3x * 2x + 2y * 2x) + -3y * (3x + 2y)) = 0

Reorder the terms:

((4xy + 6x2) + -3y * (3x + 2y)) = 0

((4xy + 6x2) + -3y * (3x + 2y)) = 0

(4xy + 6x2 + (3x * -3y + 2y * -3y)) = 0

(4xy + 6x2 + (-9xy + -6y2)) = 0

Reorder the terms:

(4xy + -9xy + 6x2 + -6y2) = 0

Combine like terms: 4xy + -9xy = -5xy

(-5xy + 6x2 + -6y2) = 0

Solving

-5xy + 6x2 + -6y2 = 0

Solving for variable 'x'.

Factor a trinomial.

(2x + -3y)(3x + 2y) = 0

Combine like terms: 2y + -2y = 0

3x + 0 = 0 + -2y

3x = 0 + -2y

Remove the zero:

3x = -2y

Divide each side by '3'.

x = -0.6666666667y

Simplifying

x = -0.6666666667y