SOLUTION: solve by substitution: 2x=2y=2 3x-y=1

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Question 163047: solve by substitution:
2x=2y=2
3x-y=1
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%282x%2B2y=2%2C3x-y=1%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

2x%2B2y=2 Start with the first equation


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


2y=-2x%2B2 Rearrange the equation


y=%28-2x%2B2%29%2F%282%29 Divide both sides by 2


y=%28%28-2%29%2F%282%29%29x%2B%282%29%2F%282%29 Break up the fraction


y=-x%2B1 Reduce



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

Since y=-x%2B1, we can now replace each y in the second equation with -x%2B1 to solve for x



3x-highlight%28%28-x%2B1%29%29=1 Plug in y=-x%2B1 into the second equation. In other words, replace each y with -x%2B1. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



3x%2Bx-1=1 Distribute the negative


4x-1=1 Combine like terms on the left side


4x=1%2B1Add 1 to both sides


4x=2 Combine like terms on the right side


x=%282%29%2F%284%29 Divide both sides by 4 to isolate x



x=1%2F2 Reduce





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


So the first part of our answer is: x=1%2F2









Since we know that x=1%2F2 we can plug it into the equation y=-x%2B1 (remember we previously solved for y in the first equation).



y=-x%2B1 Start with the equation where y was previously isolated.


y=-%281%2F2%29%2B1 Plug in x=1%2F2


y=-1%2F2%2B1 Multiply


y=1%2F2 Combine like terms (note: if you need help with fractions, check out this solver)



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


So the second part of our answer is: y=1%2F2









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

So our answers are:

x=1%2F2 and y=1%2F2

which form the ordered pair