How do you solve the following system: #3x+2y =0, 7y − 6x − 5 = 0 #?

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Answer 1 · 2016-04-03T17:12:20

#y = 5/11, x = -10/33#

Rearrange the first equation to give a value of #y# with respect to #x#.

#3x + 2y = 0#
#3x = -2y#
#-3/2x = y#

Now substitute your new value of #y# into the second equation

#7(-3/2x) - 6x - 5 = 0#
#-21/2x - 6x - 5 = 0#
#-33x - 5 = 0

Rearrange and solve for #x#

#-33/2x = 5#
#x = -10/33#

And because we know #y# with respect to #x#, we can solve

#y = -3/2x#
#y = -3/2 * -10/33 = 30/66 = 5/11#

Substitute both values into either original equation and check if it's right.

#3x + 2y = 0#
#-30/33 + 10/11 = 0#

It checks out mathematically, so it must be correct.