How do you solve $2/(3y-4)=5/(6y-7)$ ?

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Answer 1 · 2017-07-06T11:19:27

$color(magenta)(y=2$

$2/(3y-4)=5/(6y-7)$

cross multiply

$:.2(6y-7=5(3y-4))$

$:.12y-14=15y-20$

$:.12y-15y=-20+14$

$:.-3y=-6$

multiply both sides by $-1$

$:.3y=6$

$:.color(magenta)(y=2$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("Check")$

substitute $color(magenta)(y=2$

$:.2/(3(color(magenta)2)-4)=5/(6(color(magenta)2)-7)$

$:.2/(6-4)=5/(12-7)$

$:.2/2=5/5$

$:.color(magenta)(1=1$

How do you solve 2/(3y-4)=5/(6y-7)2/(3y-4)=5/(6y-7)?