Question 134232
Do you want to use substitution to solve this system?





Let's look at the first equation  {{{(1/3)x-(1/6)y=1/3}}}



{{{6((1/3)x-(1/6)y)=6(1/3)}}} Multiply both sides of the first equation by the LCD 6



{{{2x-y=2}}} Distribute



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Let's look at the second equation  {{{(1/6)x+(1/4)y=0}}}


{{{12((1/6)x+(1/4)y)=12(0)}}} Multiply both sides of the second equation by the LCD 12



{{{2x+3y=0}}} Distribute



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So our new system of equations is:


{{{system(2x-y=2,2x+3y=0)}}}




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


{{{2x-y=2}}} Start with the first equation



{{{-y=2-2x}}}  Subtract {{{2x}}} from both sides



{{{-y=-2x+2}}} Rearrange the equation



{{{y=(-2x+2)/(-1)}}} Divide both sides by {{{-1}}}



{{{y=((-2)/(-1))x+(2)/(-1)}}} Break up the fraction



{{{y=2x-2}}} Reduce




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Since {{{y=2x-2}}}, we can now replace each {{{y}}} in the second equation with {{{2x-2}}} to solve for {{{x}}}




{{{2x+3highlight((2x-2))=0}}} Plug in {{{y=2x-2}}} into the first equation. In other words, replace each {{{y}}} with {{{2x-2}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{2x+(3)(2)x+(3)(-2)=0}}} Distribute {{{3}}} to {{{2x-2}}}



{{{2x+6x-6=0}}} Multiply



{{{8x-6=0}}} Combine like terms on the left side



{{{8x=0+6}}}Add 6 to both sides



{{{8x=6}}} Combine like terms on the right side



{{{x=(6)/(8)}}} Divide both sides by 8 to isolate x




{{{x=3/4}}} Reduce






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



So the first part of our answer is: {{{x=3/4}}}










Since we know that {{{x=3/4}}} we can plug it into the equation {{{y=2x-2}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=2x-2}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=2(3/4)-2}}} Plug in {{{x=3/4}}}



{{{y=6/4-2}}} Multiply



{{{y=-1/2}}} Combine like terms and reduce.  (note: if you need help with fractions, check out this <a href="http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver">solver</a>)




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



So the second part of our answer is: {{{y=-1/2}}}










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


So our answers are:


{{{x=3/4}}} and {{{y=-1/2}}}