Question

x-1/2+y+/5=21/5,   x+y/3=y-1
3/a +4+b=2,  9/a-4/b=2
8/x-9/y=1,  10/x+6/y=7
Its simultaneous equations

Answer 1

$\frac{x-1}{2}+\frac{y+1}{5} = \frac{21}{5},\ \ \ \ Multiply\ by\ 10 \\ \\ 5x -5 +2y+2 = 42, \ \ 5x +2y = 45\ \ \ -\ equation\ 1 \\ \\ \frac{x+y}{3} = y-1,\ \ \ x+y = 3y - 3,\ \ \ x - 2y = -3 ,\ \ \ - equation\ 2 \\ \\ add\ both\ equations.,\ \ \ 6x = 45-3 = 42. \ \ x = 7 \\ Substitute\ in\ equation 2,\ \ 7-2y = -3,\ \ \ 10-2y=0,\ \ \ y=5$
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$\frac{3}{a}+\frac{4}{b}=2,\ \ \ \frac{9}{a}-\frac{4}{b}=2,\ \ \ Add\ both\ equations \\ \\ \frac{3}{a}+\frac{9}{a}+\frac{4}{b}-\frac{4}{b}=2+2 \\ \\ \frac{12}{a}=4 \\ \\ a = \frac{12}{4} = 3 ,\ \ \ substitute\ in\ 1st\ equation, \\ 1+4/b=2,\ \ \ 4/b = 1,\ \ b=4$

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$\frac{8}{x}-\frac{9}{y}=1,\ \ \ \ \ \frac{10}{x}+\frac{6}{y}=7 \\ \\ Multiply\ 1st\ equation\ by\ 2\ and\ 2nd\ by\ 3 \\ \\ \frac{16}{x}-\frac{18}{y}=2,\ \ \ \ \ \frac{30}{x}+\frac{18}{y}=21 \\ \\ Add\ both\ equations\ to\ get \\ \\ \frac{16}{x}+\frac{30}{x}-\frac{18}{y}+\frac{18}{y}=21+2 \\ \\ 46/x = 23,\ \ \ x= \frac{46}{23},\ \ \ x=2 \\ substitute\ in\ 1st\ equation \\ \\ \frac{8}{2}-\frac{9}{y}=1,\ \ \ 4-1=9/y,\ \ \ 3=9/y,\ \ \ y=3$