How do you solve for y in $x = \frac{y + 2}{5 y - 1}$ $x=(y+2)/(5y-1)$ ?

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Answer 1 · 2016-06-19T09:10:11

$y = \frac{2 + x}{5 x - 1}$ $color(blue)(y = (2 + x) / (5x - 1)$

$x = \frac{y + 2}{5 y - 1}$ $x = (color(blue)(y)+2) / (5color(blue)(y) -1)$

Our main motive in solving this question should be to isolate $y :$ $color(blue)(y:$

$x \cdot (5 y - 1) = y + 2$ $x * (5color(blue)(y) -1) = color(blue)(y)+2$

We multiply $x$ $x$ with both terms within the bracket.

$x \cdot (5 y) + x \cdot (- 1) = y + 2$ $x * (5color(blue)(y)) + x *( -1) = color(blue)(y)+2$

$5 x y - x = y + 2$ $5xcolor(blue)(y) -x = color(blue)(y)+2$

$5 x y - y = 2 + x$ $5xcolor(blue)(y) - color(blue)(y) = 2 + x$

$y (5 x - 1) = 2 + x$ $color(blue)(y)(5x - 1) = 2 + x$

$y = \frac{2 + x}{5 x - 1}$ $color(blue)(y = (2 + x) / (5x - 1)$

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