How do you solve this system of equations: #3x = 5y + 6 and - 6x + 3y = - 12#?

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Answer 1 · 2017-12-08T00:46:53

The solution is the ordered pair #(2,0)#.

We can use substitution since we know the value of #3x#. Start with the second equation:

#-6x+3y=-12\rightarrow -2(3x)+3y=-12#.

Since we know the value of #3x# we substitute:

#-2(5y+6)+3y=-12#

distribute:

#-10y-12+3y=-12#

collect like terms:

#-7y-12=-12#

add 12 and divide by #-7#:

#y=0#.

Once we know #y# we can solve for x by substitution:

#3x=5(0)+6 \rightarrow x = 2#.

So the solution is the ordered pair #(2,0)#.