Solve 2x+5y/xy=6 and 4x-5y/xy=-3
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Answer (1):
⇢ 2x + 5y = 6xy
⇢ 2x + 5y + -6xy = 6xy + -6xy
⇢ -6xy + 2x + 5y = 0
⇢ -6xy + 2x + 5y + -5y = 0 + -5y
⇢ -6xy + 2x = -5y
⇢ x (-6y + 2) = -5y
⇢ x (-6y + 2)/-6y + 2 = -5y/-6y + 2
⇢ x = -5y/-6y + 2
Answer (2):
⇢ 4x - 5 = -3xy
⇢ 4x - 5 + 3xy = -3xy + 3xy
⇢ 3xy + 4x - 5 = 0
⇢ 3xy + 4x - 5 + 5 = 0 + 5
⇢ 3xy + 4x = 5
⇢ x (3y + 4) = 5
⇢ x (3y + 4)/3y + 4 = 5/3y + 4
⇢ x = 5/3y + 4
Therefore, x = -5y/-6y + 2 and x = 5/3y + 4 is the required answer.
Note:
- I have solved for x for both equations.
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