SOLUTION: 1/3x - 1/6y =1/3 1/6x + 1/4y =0

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Do you want to use substitution to solve this system?




Let's look at the first equation


Multiply both sides of the first equation by the LCD 6


Distribute


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Let's look at the second equation

Multiply both sides of the second equation by the LCD 12


Distribute


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So our new system of equations is:





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

Start with the first equation


Subtract from both sides


Rearrange the equation


Divide both sides by


Break up the fraction


Reduce



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Since , we can now replace each in the second equation with to solve for



Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.



Distribute to


Multiply


Combine like terms on the left side


Add 6 to both sides


Combine like terms on the right side


Divide both sides by 8 to isolate x



Reduce





-----------------First Answer------------------------------


So the first part of our answer is:









Since we know that we can plug it into the equation (remember we previously solved for in the first equation).



Start with the equation where was previously isolated.


Plug in


Multiply


Combine like terms and reduce. (note: if you need help with fractions, check out this solver)



-----------------Second Answer------------------------------


So the second part of our answer is:









-----------------Summary------------------------------

So our answers are:

and