Question

3x/2+2/3=5 , 5x/4-4y/9=7/6

by susbstitution

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Answer 1

$\frac{3x}{2} + \frac{2y}{3} = 5 \\ \frac{9x + 4y}{6} = 5 \\ 9x + 4y = 30 - - (i) \\ \frac{5x}{4} - \frac{4y}{9} = \frac{7}{6} \\ \frac{45x - 16y}{36} = \frac{7}{6} \\ \frac{45x - 16y}{6} = 7 \\ 45x - 16y = 42 - - (ii) \\ multiply \: equation \: (i) \: by \: 5 : \\ 45x + 20y = 150 - - (iii) \\ subsitute \: equation \: (ii) \: in \: (iii) : \\ 45x + 20y = 150 \\ 45x - 16y = 42 \\ - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - - - - - - - \\ 36y = 108 \\ y = 3 \\ put \: the \: value \: of \: y \: in \: (i)\: equation : \\ 9x + 4 \times 3 = 30 \\ 9x + 12 = 30 \\ 9x = 18 \\ x = 2$

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