SOLUTION: Solve the following system using substitution. x+3y=8 2x-y=2

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Question 678302: Solve the following system using substitution. x+3y=8 2x-y=2
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-y=2%2Cx%2B3y=8%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-y=2 Start with the first equation


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


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


y=%28-2x%2B2%29%2F%28-1%29 Divide both sides by -1


y=%28%28-2%29%2F%28-1%29%29x%2B%282%29%2F%28-1%29 Break up the fraction


y=2x-2 Reduce


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

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


x%2B3highlight%28%282x-2%29%29=8 Plug in y=2x-2 into the second 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.


x%2B%283%29%282%29x%2B%283%29%28-2%29=8 Distribute 3 to 2x-2


x%2B6x-6=8 Multiply


7x-6=8 Combine like terms on the left side


7x=8%2B6Add 6 to both sides


7x=14 Combine like terms on the right side


x=%2814%29%2F%287%29 Divide both sides by 7 to isolate x


x=2 Divide


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


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


Since we know that x=2 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%282%29-2 Plug in x=2


y=4-2 Multiply


y=2 Combine like terms


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


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



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

So our answers are:

x=2 and y=2

which form the point