Question

(vi) 6x + 3y =6xy
2x + 4y = 5xy using reducing the variable method
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Answer 1

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Given equations are,

• 6x+3y=6xy _____(1)
• 2x+4y=5xy _____(2)

From eq (1) and (2) ×3

We get,

$\begin{gathered} \: \: 6x + 3y = 6xy \\ \: \: 6x + 12y = 15xy \\ - \: \: \: \: - \: \: \: \: \: \: \: \: \: \: - \\ - - - - - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 9y = 9xy \\ \end{gathered}$

9y-9xy = 0

9y(1-x) = 0

y(1-x) = 0

=> y = 0 or x = 1

1) If y = 0,

From (i) we get,

6x+3(0) = 6x(0)

6x = 0

=> x = 0

2) If x = 1

From (i) we get,

6(1)+3y = 6(1)y

=> 6 = 6y-3y

=> 3y = 6

=> y = 2

Hence,

x = 0 , y = 0

OR

x = 1 , y = 2

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