Question

Elimination class 10
$x + \frac{6}{y} = 6$
$3x - \frac{8}{y} = 5$
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Answer 1

$\sf Given: x\ +\ \frac{6}{y} = 6\ and\ 3x\ -\ \frac{8}{y} = 5.\\\\To\ find: The\ value\ of\ x\ and\ y.\\\\Answer:\\\\Let\ x\ +\ \frac{6}{y} = 6\ be\ equation\ 1\ and\ 3x\ -\ \frac{8}{y} = 5\ be\ equation\ 2.\\\\For\ elimination,\ we\ will\ have\ to\ make\ a\ term\ from\ both\ the\ equations\ the same\ in\ order\ to\ cancel\ it.$

$\sf Multiplying\ equation\ 1\ with\ 8.\\\\We\ get\ 8x\ +\ \frac{48}{y} = 48.\\\\Multiplying\ equation\ 2\ with\ 6\\\\We\ get\ 18x\ -\ \frac{48}{y}= 30\\\\Adding\ both\ the\ equations,\ we\ get\ 26x = 78.\\\\x = 78/26 = 3\\\\Substituting\ the\ value\ of\ x\ in\ equation\ 1.\\\\3\ +\ \frac{6}{y} = 6\\\\\\\frac{3y\ +\ 6}{y} = 6\\3y + 6 = 6y\\6 = 6y - 3y\\6 = 3y\\y = 2.\\\\Therefore, x = 3\ and\ y = 2.$