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##### Nur Syafiqah

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Solve the following simultaneous equations. How to solve this question? Please

Date Posted: 7 months ago
Views: 83
J
7 months ago
2x - 3y = 6 ①

So 2x = 3y + 6

x = 3/2 y + 3 → ②

From question, 4x + 6y = 3xy → ③

Substitute ② into ③,

4(3/2 y + 3) + 6y = 3(3/2 y + 3)y

6y + 12 + 6y = 9/2 y² + 9y

9/2 y² - 3y - 12 = 0

9y² - 6y - 24 = 0

3y² - 2y - 8 = 0

(3y + 4)(y - 2) = 0

3y + 4 = 0 or y - 2 = 0
3y = -4 or y = 2
y = -4/3
= -1⅓

So x = 3/2(-4/3) + 3 or x = 3/2(2) + 3

x = 1 or x = 6

Therefore,

x = 1, y = -1⅓, or x = 6, y = 2
J
7 months ago
Or you can start from solving x first.

2x - 3y = 6 ①

So 3y = 2x - 6

y = ⅔x - 2 → ②

From question, 4x + 6y = 3xy → ③

Substitute ② into ③,

4x + 6(⅔x - 2) = 3x(⅔x - 2)

4x + 4x - 12 = 2x² - 6x

2x² - 14x + 12 = 0

x² - 7x + 6 = 0

(x - 1)(x - 6) = 0

x - 1 = 0 or x - 6 = 0
x = 1 or x = 6

So y = ⅔(1) - 2 or y = ⅔(6) - 2

y = -1⅓ or y = 2

Therefore,

x = 1, y = -1⅓, or x = 6, y = 2 