You can put this solution on YOUR website! first clear of fractions then solve using substitution
x/2 - y/3= 5/6
x/5 - y/4= 29/10
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I wouldn't do it that way, but...
Multiply the 1st eqn by 6 & and the 2nd by 20
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3x - 2y = 5
4x - 5y = 58
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Multiply the 1st eqn by 4 and the 2nd by 3
12x - 8y = 20 --> 12x = 8y+20
12x -15y = 174
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Sub for 12x in the 2nd eqn
(8y+20) - 15y = 174
-7y = 154
y = -22
etc