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Solve the following simultaneous equations. How to solve this question? Please
Date Posted: 5 years ago
Views: 983
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
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
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
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
See 1 Answer
done
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clear
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tip: use substitution method instead of elimination method because of the xy in equation 2
Date Posted:
5 years ago
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