Answer:
see explanation
Step-by-step explanation:
Given the 2 equations
A = x² + xy + 2y - 1 → (1)
A + B = 2x² - xy - 4y - 1 → (2)
From (2)
B = 2x² - xy - 4y - 1 - A
= 2x² - xy - 4y - 1 - (x² + xy + 2y - 1) ← distribute parenthesis
= 2x² - xy - 4y - 1 - x² - xy - 2y + 1 ← collect like terms
= x² - 2xy - 6y
Hence
A - B = x² + xy + 2y - 1 - (x² - 2xy - 6y) ← distribute parenthesis
= x² + xy + 2y - 1 - x² + 2xy + 6y ← collect like terms
= 3xy + 8y - 1
(b)
Given A - B = x, then
x = 3xy + 8y - 1 ( add 1 to both sides )
x + 1 = 3xy + 8y ← factor out y from each term
x + 1 = y(3x + 8) ← divide both sides by (3x + 8)
y = [tex]\frac{x+1}{3x+8}[/tex]
