SOLUTION: Solve using elimination method please. -6x+y=0 9x-12y=2 please solve ending with ordered pair please. thank you!!

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Question 176207: Solve using elimination method please.

-6x+y=0
9x-12y=2

please solve ending with ordered pair please. thank you!!
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(48568) About Me  (Show Source):
You can put this solution on YOUR website!
-6x+y=0
9x-12y=2
-----------
Multiply 1st by 12 to get:
-72x + 12y = 0
9x - 12y = 2
-----------------
Add to solve for "x":
-63x = 2
x = -(-/63)
--------------
Substitute into y = 6x to solve for "y":
y = 6(-2/63) = -12/63
-------------------------
Ordered Pair: (-2/63,-12/63)
================================
Cheers,
Stan H.

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%28-6x%2By=0%2C9x-12y=2%29


12%28-6x%2By%29=12%280%29 Multiply the both sides of the first equation by 12.


-72x%2B12y=0 Distribute and multiply.


So we have the new system of equations:
system%28-72x%2B12y=0%2C9x-12y=2%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28-72x%2B12y%29%2B%289x-12y%29=%280%29%2B%282%29


%28-72x%2B9x%29%2B%2812y%2B-12y%29=0%2B2 Group like terms.


-63x%2B0y=2 Combine like terms.


-63x=2 Simplify.


x=%282%29%2F%28-63%29 Divide both sides by -63 to isolate x.


x=-2%2F63 Reduce.


------------------------------------------------------------------


-72x%2B12y=0 Now go back to the first equation.


-72%28-2%2F63%29%2B12y=0 Plug in x=-2%2F63.


16%2F7%2B12y=0 Multiply.


7%2816%2Fcross%287%29%2B12y%29=7%280%29 Multiply both sides by the LCD 7 to clear any fractions.


16%2B84y=0 Distribute and multiply.


84y=0-16 Subtract 16 from both sides.


84y=-16 Combine like terms on the right side.


y=%28-16%29%2F%2884%29 Divide both sides by 84 to isolate y.


y=-4%2F21 Reduce.


==================================
Answer:

So the solutions are x=-2%2F63 and y=-4%2F21


which form the ordered pair