# How do you solve the system #x/2-y/3=5/6# and #x/5-y/4=71/10#?

##### 1 Answer

Mar 21, 2016

Scale and combine the equations to eliminate

#{ (x = -37), (y = -58) :}#

#### Explanation:

Given:

#{ (x/2-y/3=5/6), (x/5-y/4=71/10) :}#

Multiply the first equation by

#{ (3x-2y=5), (4x-5y=142) :}#

To eliminate

#{(15x-10y=25),(8x-10y=284):}#

#=> 7x = 25-284 = -259#

Then divide both ends by

#x = -259/7 = -37#

Substitute this value of

#-111-2y=5#

Add

#-2y=116#

Divide both sides by

#y = -58#