SOLUTION: 3x-y=4 -9x+3y=-12

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Question 127298: 3x-y=4
-9x+3y=-12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:

system%283x-y=4%2C-9x%2B3y=-12%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

3x-y=4 Start with the first equation


-y=4-3x Subtract 3x from both sides


-y=-3x%2B4 Rearrange the equation


y=%28-3x%2B4%29%2F%28-1%29 Divide both sides by -1


y=%28%28-3%29%2F%28-1%29%29x%2B%284%29%2F%28-1%29 Break up the fraction


y=3x-4 Reduce



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

Since y=3x-4, we can now replace each y in the second equation with 3x-4 to solve for x



-9x%2B3highlight%28%283x-4%29%29=-12 Plug in y=3x-4 into the first equation. In other words, replace each y with 3x-4. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



-9x%2B%283%29%283%29x%2B%283%29%28-4%29=-12 Distribute 3 to 3x-4


-9x%2B9x-12=-12 Multiply


-12=-12 Combine like terms on the left side


0=-12%2B12Add 12 to both sides


0=0 Combine like terms on the right side




Since this equation is always true for any x value, this means x can equal any number. So there are an infinite number of solutions.