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