Question

1/3x-1/4y+1=0:1/5x+1/2y=4/5​

Answer 1

Step-by-step explanation:

$\frac{1}{3x} - \frac{1}{4y} = 0 \\ \frac{4y - 3x}{12xy} = 0 \\ 4y - 3x = 0 \: - - (i)\\ \frac{1}{5x} + \frac{1}{2y} = \frac{4}{5} \\ \frac{2y + 5x}{10xy} = \frac{4}{5} \\ 2y + 5x = \frac{4 \times 10xy}{5} \\ 2y + 5x = 8xy\: - - (ii) \\ multiply \: equation \: (ii) \: b y\: 2 : \\ 4y + 10x = 16xy \: - - (iii) \\ subtract \: equation \: (i) \: in \: (iii) : \\ 4y + 10x = 16xy \\ 4y - 3x = 0 \\ - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - - - - - \\ 7x = 16xy \\ y = \frac{7}{16} \\ put \: the \: value \: of \: y \: in \: eq \: (i) : \\ 4 \times \frac{7}{16} - 3x = 0 \\ \frac{7}{4} = 3x \\ x = \frac{7}{12}$

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